In most cases, the leading zero probably doesn't hurt except to take
more airtime.

At your runway, however, "zero two" could easily be confused with "two
zero," which as you know is the opposite end of the same runway. Most
listeners will understand where you are and where you're going, but
watch out for that student pilot on his solo cross country who's about
to join the downwind for a right-hand runway 20 pattern!