Is the "Gems" update going to affect the desktop version?
Will it only change the Android and iOS apps, or is the website also going to be updated?
Most of the updates they've brought to the mobile app (bots, tap-matching, sentences selected from a list of words) haven't been brought to desktop. Considering the unanimous negative feedback, they'll probably remove it from the mobile version within a few months, much less bring it to desktop.
Unlike a different set of exercises, having different currencies on different platforms doesn't make sense (since they are synced anyway). The question is which one they will stick with.
Considering the unanimous negative feedback, they'll probably remove it
That's not what history has taught us.
They haven't said, so all we can do is speculate.
However, it would make little sense to have two virtual currencies (in the long term).
So I assume that if they come up with a version of Gems that they are happy with, then they will roll it out for everyone and on all platforms (well those they are still maintaining). Note that this is a revenue generation play, as you can buy Gems for real money. So they may do this even if It is unpopular.