Absolutely. I do it a lot, generally with the middle finger as my index is tied up with the pick. I've never been able to tremolo-pick very fast, maybe because I'm left-handed playing right-handed, but I can do it with that middle finger. Dick Dale was my first influence on guitar, and when I need to do that double-picked surf thing, I always use the middle finger. If I have a big crescendo chordal ending to play, I'll do it with the middle finger and sometimes add in the ring finger, sort of a modified rasgueado technique. If I had it to do all over again, I might never have used a pick at all--I love what Mark Knopfler and Jeff Beck do with thumb and fingers.
That being said, when I play bass I use a pick--my index finger actually has a permanent bend at the first knuckle from 50 years of picking (guitar, not much bass.)