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Absolutely. I just gotta get past the mental hurdle of approaching women and realize that women in college are waiting for that bold guy to come up and talk to them.
And in your situation on the small campus, framing your interactions in your mind more as "grazes" than "approaches" could help; you want to be chatty, friendly with everyone, guys & girls in this situation. Not that you don't want to do a full on pickup when it makes sense: If there is a good vibe with a girl, take her #.
You are correct in that on a campus that size if you are just an overt approach machine 24/7 your rep could deflate (as in making it look obvious that you are approaching with telling all 1000 girls on campus "hi, my names X i think you're cute" as opposed to making number-taking a part of your daily routine of having normal convos with people).