Ok I found a few guitar forums where my same question was asked (using one of those bluetooth transmitters on the headphone output of an amp). The general consensus was, don't do it! Latency issues.
It makes sense though, first your BT transmitter has to package the analog signal to bluetooth, send it through the air, and your bluetooth headphone has to convert it back to analog. Well that's alot of processing taking place, and when you pluck a guitar string, you have to hear the sound instantly. Any bit of delay could range from annoying to completely unnaceptable.
So I'll be going with wired headphones.
Why would the quality be any different than the quality between a wireless transmitter/receiver for a guitar? Those work fine. In fact I'm using a wireless setup with the guitar and there is no latency or distortion and it has to go through the same packing/unpacking you describe.
