Recent supporting work
In a paper published in the Jan 2017 issue of Nature Neuroscience, Wei Li and colleagues propose a mechanism that supports the "reverse learning" process based on dendritic calcium spikes that regulate spine formation.
However, as the authors discuss, the implications of their findings are more nuanced. They support the idea of reverse learning but show that it is not the only thing going on in REM sleep:
REM sleep is not simply a substitute for wakefulness to stimulate plasticity, for pruning synapses during development or for persevering genetic identities of neuronal circuits. Instead, REM sleep is important for selectively incorporating new synapses into the existing circuits. It could be viewed as a “selection committee” for building and maintaining the synaptic network.
If we accept that reverse learning functions by the proposed mechanism, I would guess it would not be perturbed significantly by dream recall. This is because the calcium spikes in their experiments occurred on the order of seconds, and only during REM sleep. Dream recall, on the other hand, is is a high-level mental process that is probably restricted to humans.
This is just my best intuitive guess. For all we know, any neural event anywhere in the brain can potentially influence a subsequent event anywhere else in the brain, so really all bets are still on the table.