"Fit" is important in any organization and is among those intangible reasons that people are accepted or rejected from nearly any kind of organization. It may be unusual for a heavily tattooed person to go through rush at your school, but I would say that what's most important here is for you to try while putting your best foot forward.
Playing it more conservative will help you throughout your life. If you mean visible tats like Lil Wayne, you might have a problem. But if you mean behind your ear, around your wrist, etc, you might have creative means at your disposal to conceal them (hairstyle?) or draw attention away from them.
The National President of GXP is a Delta who I would consider to be heavily tatted also and I don't recall her having any issues when she went through. Similarly, the national executive director had dreadlocks when he was pursuing Alpha. He, also, had concerns about coming across as conservative enough. Needless to say, he made it, too.
Good luck. If you know of any artists on your campus who would like an org like ours, let us know.
