it's very important for musicians to wear clothes. for in this day and age, how many of the bands (as in all of their members) have you seen playing onstage butt-naked?
nah kidding. i don't know. all boils down to perception. see, if it's a really heavy metal band, you'd expect them to have long hair, goatees, tats, body paint, masks, tattered jeans, tattered shirts, and everything else tattered... creates this "wtf do you guys care about we wear attitude?!" 'course, doesn't necessarily apply to all. but the common masses see these dudes as part of the metal music industry.
then there's the so-called, overrated 'emo' bands we see nowadays. tight jeans, tight shirts, multi - colored whatnots on top of their black whatelses. sidebangs, accessories, the works. we instantly associate them with 'islas-my-wrists, wailing, whining vocals and lyrics' just because they look like that. and then we label the genre as emo. no-no.
i could go on, and on. but then again, to answer the TS's question, i would say that in more ways than one, it can be important. at least, to those of us who doesn't know much about music. to us who can only mosh, sit amidst tables with beer bottles on 'em and chainsmoke our lungs off, and listen to the music that these musicians play, it's hard not to at least check out what 'em musikeros are wearing while playing. because that's what we instantly see. we can only watch, and gawk (frustrated musicians that we are)
and like what the others have said before me, it doesn't really matter what you wear, as long as you like what you're wearing, as long as you're comfortable in it. and you, (yes you) you're not there to impress them with your branded clothes or bling-blings or whatever you call it, in the first place. the primary reason why you're playing what you're playing is because you love what you do, and you're damn good at it.