Well you *can* do that (and I've seen it done that way), but
often - the music being improvised anyway - you don't really
have a tempo indication, except for Swing, Med. Swing, Uptempo
Swing, Ballad etc., and those are just suggestions or show how
the piece was played in a referenced recording. That's, if we're
talking about a lead sheet - look into a "Real Book" for
examples.
If it's orchestral music (eg Big Band), the score probably
contains more exact tempo values (which my Big Band conductor
usually ignores ...).
______
Don't
ask me who's influenced me. A lion is made up of the lambs
he's digested, and I've been reading all my life.
--
Giorgos Seferis