Depends how you mount them. A lot of guys run "rock lights" which are underbody ligths specifically for offroading, so you can light up and see what you're navigating over. I think FROADER runs them now or ran them in the past.
If they're LED light strips and tucked way up under the body, you're fine. If they're mounted low and are glass housings, they're not gonna last through any serious offroading. Also keep in mind that if you go through any mud & water, you're going to cover them and potentially ruin any connections. Mud and water crossings are a whole different ballgame from rock crawling.
Bottom line: if you tuck the lights up and do some rockcrawling, you'll be fine. Any water crossings or mudding, and you'll coat EVERYTHING under there and they won't last.