I have the Slig Barracks logo on the back of my personalized T-Shirt, and it is kinda cool. The thing about tattoos is, you can't take them off (temporarily). Unlike clothes.
Getting a tattoo is a long-term commitment and I would only recommend it if you are a true Oddworld fan through and through, and I would only suggest torso or back tattoos, which are the easiest to cover up.
There's plenty of other ways to show your devotion to Oddworld, merchandise, artwork, home-made Slig finger puppets... Heck you can probably get a temporary transfer tattoo done first, and see what you think of it. If you don't like it, you can always say no

.