Well, to be able to answer your question affirmatively, we'd have to know all the effects of sleep deprivation, including the long term ones, and those are still are not fully accounted for.
However I did find some more recent research that addresses the question of weekend sleep recover on some parameters. Pejovic et al. found (quoting from the abstract):
Serial 24-h IL-6 plasma levels increased significantly during sleep restriction and returned to baseline after recovery sleep. Serial 24-h cortisol levels during restriction did not change compared with baseline, but after recovery they were significantly lower. Subjective and objective sleepiness increased significantly after restriction and returned to baseline after recovery. In contrast, performance deteriorated significantly after restriction and did not improve after recovery. Extended recovery sleep over the weekend reverses the impact of one work week of mild sleep restriction on daytime sleepiness, fatigue, and IL-6 levels, reduces cortisol levels, but does not correct performance deficits. The long-term effects of a repeated sleep restriction/sleep recovery weekly cycle in humans remain unknown.
The good news is that on most measures there was recovery after the weekend, and this is consistent with other studies e.g. with that by Faraut on hormonal measures. I still find their performance finding rather shocking, so it's perhaps worth taking note at exactly what performance they looked at; it was basically just the PVT:
It's indeed a good question how many more nights of leisurely sleep would cause PVT to recover. I strongly doubt the impairment is permanent. Alas the study by Pejovic et al. didn't have any follow-up after the weekend.
A similar study was conducted prior by Banks et al., and they made a prediction on PVT recovery, but it still hasn't been confirmed
Neurobehavioral deficits induced by 5 nights of sleep restricted to 4 h improved monotonically as acute recovery sleep dose increased, but some deficits remained after 10 h TIB [time in bed -- my note] for recovery. Complete recovery from such sleep restriction may require a longer sleep period during 1 night, and/or multiple nights of recovery sleep. [...]
PVT fastest reaction times were projected to require a sleep dose of more than 13 h TIB (11 h TST [total sleep time -- my note]) to intersect the control condition. However, the confidence intervals for intersection with control group levels were large for all outcomes presented
I found one more recent animal study on the matter, by Deurveilher et al., which used a rat version of PVT, with rather different results
A 28-h period of the 3/1 chronic sleep restriction (CSR) protocol [sleep reduced to ~60% of normal as result of this protocol -- my note] disrupted performance on a sustained attention task in rats, as sleep deprivation does in humans. Performance improved after longer [one week -- my note] periods of CSR, suggesting allostatic adaptation, contrary to some reports of progressive deterioration in psychomotor vigilance task performance during CSR in humans. However, as observed in humans, there were individual differences among rats in the vulnerability of their attention performance to CSR.
Below are the graphs from the paper on the week-long CSR, which shows the remarkable allostatic adaptation on PVT, but not on weight loss.
So I'm guessing the jury is still out how quickly humans recover or if they may even adapt to sleep deprivation on PVT. I'm guessing that given the other effects of sleep deprivation, controlled longer-term studies in humans are probably going to be difficult to come by...
I've also consulted the 6th edition (2017) of Principles and Practice of Sleep Medicine; its chapter on sleep deprivation (and recovery) has among its authors two of the co-authors (the lead and the PI--Dinges) of the Banks study I already mentioned. So its conclusion are somewhat similar.
Few studies have examined recovery sleep after periods of
sleep restriction. [...] Although participants felt that their functioning
was restored, with subjective reports of sleepiness and
performance recovering to baseline, subjective measures do
not appear to accurately parallel objective measures of neurobehavioral
recovery. These findings suggest that more than
2 or 3 nights of extended sleep may be needed to return neurobehavioral
functions to baseline levels. [...] Overall, work to date suggests that complete recovery from
a period of sleep restriction may necessitate a sleep opportunity
of more than 10 hours or more than 3 days if sleep is
restricted to 8 hours a night. In addition, different aspects of
performance and neurobehavioral function appear to recover
at different rates, with different trajectories.
That combination finding is additional based one other study they highlight, by Rupp et al., which did look at longer recovery periods; the summary from the book
Rupp et al extended the recovery period
to five 8-hour sleep opportunities, following a week of sleep
restricted to 3 hours of time in bed each night. Despite the
extra recovery nights, performance still failed to return to
baseline levels. In a second group that extended their sleep
prophylactically to 10 hours of time in bed before the period
of sleep restriction, performance declined at a slower rate and
recovered to baseline more quickly, suggesting that sleep
restriction and recovery vary as a function of prior sleep.
Therefore, sleep extension or supplemental nap sleeps can be
used as a prophylactic measure or countermeasure to lessen
the performance effects of sleep deprivation during periods of
extended wakefulness or sleep deprivation.
Looking at the actual article, the 5 recovery days were 8 h TIB (probably because the author works at an army hospital), which for me personally would still count as mild sleep deprivation (less than 8 hrs actual sleep = TST), and which is somewhat odd contrast with opening statement in the paper that 8 hours of actual sleep are considered non-deprived. But that seems to be the only study using a longer recovery period to date. Below is a graph from that paper:
The two tests are part of PVT. And description of the two groups:
“Extension” group (nightly TIB = 10 h) or a “Habitual” sleep group (usual nightly TIB).
To determine Habitual Sleep schedules for volunteers assigned to the Habitual Group, actigraphic estimated total sleep time on weeknights (Sunday through Thursday nights; nights excluded if followed by a holiday or weekend) was determined, and 15 min were added to the average (to avoid inadvertently sleep restricting volunteers) and rounded up to the nearest 5 min for the final TIB amount. Bedtime was determined by subtracting TIB from the 07:00 rise time (i.e., a subject averaging 7 hours 15 min of sleep would have a bedtime of 23:45).
Frankly I find that being able to bank on sleep prior to deprivation, not just recover it thereafter, even more interesting. Also despite the obvious (and statistically significant) difference in PVT between groups,
No group differences in subjective sleepiness were evident during any phase of the study.
And also another finding
For both PVT variables, younger individuals showed a steeper slope of performance deterioration during sleep restriction and steeper slopes of improvement during the transition from sleep restriction to recovery and during recovery compared to older individuals.
Honestly I'm a bit concerned about overfitting because this was a small study (two dozen participants). However they say in their discussion of related research that this observed interaction/influence (of age) is consistent with other studies. Perhaps it goes along with the received wisdom that older people [need to] sleep less.
Another paper derived from the same study of Rupp et al. looked at math throughput and task acquisition (tested using ANAM, which presents a significant learning effect) and found that their observations mostly mirror those for PVT, except that presleep wasn't as significant as recovery sleep for this math/learning test.
Finally, it's generally accepted (see e.g. Pilcher and Huffcutt) that sleep deprivation influences mood even more than either cognitive or motor performance, however it seems that the recovery is quicker (perhaps owing to the hormonal one?), at least in older people, cf. Reynolds et al.:
While the increase [in Total Mood Disturbance -- my note] tended to be greater in women, in both groups self-ratings of mood returned to baseline after 1 night of recovery sleep.