The levels that were on my trailer when I bought it were attached with only the adhesive. (No screws). I lost one to highway winds on my most recent sojourn.
The one I bought to replace it also came with adhesive. I too am hesitant about putting holes in my fiberglass, although I know that is an unreasonable fear. The problem with the adhesive method is that it is an adhesive FOAM, and it doesn't give you a rock-solid attachment. In other words, in spite of my very-careful installation on a perfectly level trailer, the level can rotate small amounts. To be totally reliable, it has to be calibrated (leveled) before you can rely on it. Each time.
Did you know that your iPhone has an app that is a level? Its in the "extras" app. It's "behind" the compass. Very useful to know.
-Speak