no, but there is a lot to it that if you like the way someone else sounds then of course we find out what they use and even tho we all have our own sounds you may get in the same neighborhood at least.
a pro sax player friend of mine uses a beechler on his selmar, and you are right, it has a very distinct flavour, it’s a really expressive mouthpiece – brings out a lot of exagerated feeling, i would say more jazzy than rock but can be a very loud projecting mouthpiece- i think it took him several weeks to get used to it embouchure wise.
when it comes to setups i think there are only 3 basic setups (IMHO) – rock&roll, jazz & classical.
to me a rock/roll setup doesn’t suit jazz & classical music, like a classical setup doesn’t suit rock&roll. However a jazz setup can get into all 3, a classical can get into jazz.