I'm not trying to play devil's advocate here, even though it may sound like I am.
There is an excellent point made about alumnae. To the generation ahead of those of us currently in college, tattoos and piercings (besides your ears) aren't very classy. Some people (young and older... not OLD
) still think that tattoos are for bikers. One of the things that I've learned as a sister is that you respect your alumnae. You may not do everything they recommend, but you listen to and respect their opinions, just as you do the rest of your sisters. But like someone said, at a large school, you could be borderline for a group because you had a bad night or something, and be cut because that's the one thing that pushes them over.
We almost cut a girl from Student Ambassadors because she had a lip ring. Our advisor was very turned off by it, and we were a little surprised. Our school isn't a super conservative SEC school, and our organization isn't based on looks whatsoever, but it was something that we were worried parents checking out the school would be put off by. However, your tattoo sounds a lot easier to cover up than a lip ring.
I don't think it's shallow to wear sleeves but feel free to talk about them if someone asks. I would also make sure that if you don't wear sleeves, do not let the tattoos become a focal point of conversation. People will just remember you as "tattoo girl" and not YOU. We had a girl who only talked about Care Bears when I went through and both groups cut her because it was ALL SHE TALKED ABOUT. Therefore it was what she was associated with.