You're describing an Envelope Follower...but I'll bet it would be easy enough to wire up the detector in a compressor (or limiter) to output a voltage which could be assigned externally, rather than having that voltage control the internal gain reduction element. But I don't know of any commercially available dynamics processors that offer that feature. (At least, not in the hardware realm; I'm pretty out-of-the-loop when it comes to plugins.)
I have long yearned to be "that guy" in a live ensemble: Gimme a mixer with a crap-ton of inputs and aux sends, gimme all my pedals (or at least all my looping delays), and gimme a band of adventurous and daring improvisors with big ears. I'm not going to play a single note; I'm just going to process (and/or re-play) stuff that everyone else in the band plays.
I know plenty of musicians who'd be into it, and I have all the gear (the Yamaha 01V or the Roland M-240 mixers that have been gathering dust in my studio for several years would be ideal candidates)...just haven't had the opportunity. Or, frankly, a pressing desire to haul even more gear to a gig!