I would probably still keep synthetics moist if I used them, as I wouldn't want to store wine different ways, easier to keep everything the same.
But back in my original period of winemaking, gave parents a bunch of wine, and half of one case got lost in basement. Found it three years later, they'd been upright that whole time with synthetic corks, and there was no shrinking of cork, no leaking, no loss of wine, etc. So certainly seemed like they were alright without keeping the corks m oist. I sure wouldn't do that with a natural cork. Of course, I didn't mean to do that with these synthetic corks.