Yes, I save the drafts to a local relay (for privacy). I think most clients save to a database or cache, but I prefer using relays, where possible.

Once it's done, I publish to my personal cloud relay and then broadcoast from there (or not, I sometimes leave things only for the people I share a relay with, as not everything I post online is meant to be publicly viewable, and my cloud really is AUTH-TO-READ).