Only if you're really, really good.....
No seriously, I am technically self-taught, on bass at least. I DID have a few years training on piano and voice, with lots of ear training by the vocal coach, which has served me well.
My bass training consisted of following around my local bass hero, who worked in a popular club band around here for years, and just absorbing as much as I could. Then applying what I learned as I practiced playing along with my favorite CD's.
The result is mixed. People like my playing. I can hang with most pro situations. Done my share of recording.
But I can't read. I probably could have had a real career if I'd learned. And, poor technique early on caused physical problems later, which I'm still paying for.
If I could do it again, I'd start by getting a REALLY GOOD teacher, to avert the reading and technique problems at least.