Originally Posted by
Skyblade
Yep. If a scenario pops up randomly after a fight, you can't really be sure how long it will last or what it might entail. Save Points generally appear before bosses and important story elements. The urge to save is a fairly automatic one (as is asking her name, and getting caught by the naming screen transition). Heck, even if you wait until after finishing the conversation, she takes your money if you save before leaving the screen.
I've experimented with Yuffie a lot. I think Vincent and Cid's dialogue are the only parts of that scene I've never seen.