Is there any scientific evidence that nootropics improve synaptic plasticity / learning ability?
I'll have to leave it to someone else to provide real expert advice and references on this point but I do offer the following skeptical points.

Brain Training Doesn't Work

To my knowledge, there is no reliable data whatsoever that says domain general brain-training has any effect. Basically, you can spend as long as you like practice pitch recognition, or anagrams, or any other cognitive task, but the transfer to unpracticed tasks will be minimal - you'll simply improve at the task you've practiced. You cannot increase IQ/Working Memory/Cognitive Capacity in this way. See, for example, Owen et al, 2010. The only benefit accrued from these games is in cases of cognitive decline, such as dementia, Alzheimers, and other neurodegenerative conditions, where training can slow decline.

Nootropic Drugs Don't Work

I've seen no evidence, ever, that shows long term benefits of nootropics, beyond the usual, possibly valid claims about fatty acids found in fish. I can't find references for this right now, unfortunately, but really the onus is on those who claim that these supplements do have an effect to point to unbiased evidence.