Hi, thanks for your reply.
In the meanwhile I fiddled with this and managed to get exactly what I wanted. Let me explain.
I have ReaGate on the Snare track set to send MIDI note.
Then I use ReaLearn and map the MIDI note to Actions 1134: Transport: Tap Tempo.
I changed Project Settings, Timebase to Time, so that BPM change does not affect audio.
Then I add a delay plugin synced to project tempo. This turned out to be tricky as most plugins have artifacts when the tempo changes and they internally readjust with audible side effects.
After trying several delays I settled on OhmBoyz which handles tempo changes with no problems. Furthermore it seems to be smart enough to figure out to convert slow tempos to double time, so in stead of project tempo of say 38 it uses double, 76.
Having set all of the above I played various songs from last gig and was thrilled that in almost all cases it produced delays rhythmically related to actual track.
Basically it sounds exactly as I hoped, same as if you had someone tapping tempo manually whole night