Quite simply? Yes, but the odds are much slimmer than synthesis skillups. But it does happen. I was skilling up an alt on smithing, decided to zap some scale armor I'd just made...and bing, .2 smithing skillup to 15. Happens later as well, back when I was doing green ribbons on Kyreth for CC I can clearly remember picking up nearly a full point's worth of skill breaking the ribbons back down into silk thread.
Alas, poor FFXIClopedia. It's end was writ in greed and lulz, and ended with a /.