There is some truth to dopamine correlating with heightened motivation (but dopamine can also be too much of a good thing, such in the case of behavioral addictions, like pathological gambling, especially the presumed iatrogenic kind) However, tiredness or more prceisely sleep depravation affects dopamine receptors so it will impair many brain functions besides motivation. So the advice is probably far more straightforward to formulate as "don't waste your good hours with distractions only to get to work when you're tired".
Furthermore, if the hypodopaminergia hypothesis for ADHD is true, then "preserve your dopamine by not getting distracted" is cart-before-the horse advice since under this etiological assumption, the low-dopamine condition is the cause of distractibility rather than its effect.
There's somehting to be said aobut the kinds of distractions you list:
Today's society is pleasure seeking. We expect to obtain pleasurable experiences fast and easily. We are used to hyper-palatable foods and drinks, and we can get pornography, games and gadgets whenever we want them. The problem: with this type of pleasure-maximizing choice behaviour we may be turning ourselves into mindless pleasure junkies, handing over our free will for the next dopamine shoot. Pleasure-only activities are fun. In excess, however, such activities might have negative effects on our biopsychological health: they provoke a change in the neural mechanisms underlying choice behaviour. Choice behaviour becomes biased towards short-term pleasure-maximizing goals, just as in the addicted brain (modulated by the amygdala, posterior ventromedial prefrontal cortex' (VMPFC), striatum, nucleus accumbens; ‘A-system’) and away from long-term prosperity and general well-being maximizing objectives (normally ensured by the insula, anterior VMPFC, hippocampus, dorsolateral prefrontal cortex (DLPFC), anterior cingulate cortex (ACC); ‘I-system‘).
This is not something revolutionary. It's well known that a temporal discounting function is encoded in brains as adaptation/response to the schedule of rewards over time. This almost certainly involves more complex processes (such as long term potentiation and other forms of plasticity) than a simple reservoir-of-dopamine model.
There are certainly researchers looking into behavioral addictions in general, and in particular internet pornography addiction, interet gaming disorder and social-media addiction, but insofar these haven't received the wider acceptance that comes with blessing of being included in the DSM, ICD and so forth (except for gamblig addiction).