I'm mostly self taught with the piano. I've only played for ~12 months.
When I learned began playing, I didn't learn which notes were in what position on the staff (I only recognize a couple of notes instantly).
Instead, I typically play using the intervals between notes starting with the beginning. So instead of thinking C->E with my right hand (c position), I know I began with my thumb on the C key and move two up to play the next note with my middle finger -- I typically won't recognize any successive notes.
But my real fear is that this method is damaging for me in the long run -- Is this a bad way to approach reading music? Will it be a big detriment if I want to improv?