Welcome, Maxim. Even wretched brass players are welcome here.

Yes, I've done a bit of jazz improv on recorder. I'd say the main problem I found was trying to play over charts for Bb/Eb instruments, which often puts you in recorder-unfriendly keys. So choose a chart in a key/mode with one flat/two sharps max (assuming a C recorder), and you're probably OK. Even then, the chromatic cross-fingerings can be awkward if you're not a regular recorder player. So be sure to practice-run your chromatic scales and whatever scales/modes you plan to use in advance, to give your fingers a fighting chance.
BTW, the principal French hornist with the San Diego Symphony is also one of the finest Irish trad wind players around, on uilleann pipes, flute and whistle. So there's always hope.
Good luck, have fun!
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