Yeah, I think once you reach a certain level in your journey as a musician, you put your own sonic imprint on everything you play, with minor variations based on the instrument, amp, acoustics, etc. I would go one step further and say "tone" is born in the brain, even before the fingers can exact any influence. My whole purpose in playing music since the day I picked up the '65 Mustang my old man handed me at 15 years old was to be able to replicate the notes, rhythms, melodies and harmonies that were already floating around in my oversized melon head. It took a long time to be able to think something and then turn it into music and do it well. I'm always so much more creative writing music WITHOUT an instrument in my hand, rather than sitting there noodling in the same old patterns. I think the very best players take whatever instrument, be it guitar or whatever else, and put their soul into it. It's something that we all can hear instantly, and there is nothing more satisfying than knowing without a doubt, you can put that out there without aping someone or something else. I used to (and still do) get so bored and discouraged playing cover songs, even little riffs, because no matter how perfect you get it down, it's not yours, and its not YOU.
Hey Brandon, I'm not schooled either, but come on, man, you gotta know what KEY your in, at the very least. I taught myself music theory thanks to the local bookstore, and it changed the way I looked at music, played music, though about music...I still have trouble reading and writing (MUSIC, not words!) and I know that is holding me back...but I know how it is, it's more fun to just PLAY! But do learn to count 4/4 time at least and the keys of the songs. Your bandmates will thank you.