I was a member of the Collins Living-Learning Center improv troupe for several years, and have taken a few improv classes since then, but don’t consider these formal training since I was primarily goofing off.
I’m partial to improv that tells a story rather than improv that demonstrates mental dexterity and cleverness. The former seems more interesting for players and audience, while the latter has a whiff of showing off about it. Or maybe it’s just that I suck at the latter?
All wacky kidding aside, I consider theatrical improv training fundamental to musical improv. Anything that connects the body with the music is extremely beneficial.