Yes. We profiled the amp with a Les Paul and, after some refining, was spot on. Then, we stored the profile and changed the guitar to a 335. With the 335, the profile and the amp were different (not bad, but different) so we decided to profile again and made a different profile for the 335.
Mhhh... of course the amp will sound different if you play different guitars through it, but the physical presence of an instrument during the profiling operation won't affect the profile (not talking about refining here of course).
OTOH, if you play the profile with two different guitar you'll get two different sound, exactly as if you were using them on the profiled amp