I'm not sure I understand what you're asking...
So long as you press down the string and then make it vibrate somehow, it doesn't matter how you do it. All that'll change with the different methods is the sound and how easily you can play. i.e. I could play the bass with a rubber eraser, but I would be crap at it and it would probably sound weird.
Edit: If what you're asking is whether the thumb is a viable option for picking notes, then the answer is yes. Playing with your thumb and fingers is called Spanish playing if I'm not mistaken. I don't normally use my thumb much; but it comes in handy in some songs, like Portrait of Tracy.