I imagine he does not. The Lonely Sharptooth episode seems to be painted in this direction. The scene where Chomper attempts to befriend another sharptooth child in particular is what is most revealing. Chomper has a complete lack of social skills regarding communicating with the child. He's speaking full on leaf-eater with him and is trying to get him to play a game he's obviously not familiar with. If Chomper did have sharpteeth friends, he would have been better able to interact with the child that wouldn't have resulted in him getting chased by the sharptooth child's parents.
You could say that Chomper befriended leaf-eater speaking sharpteeth, but what are the odds of that? From what I recall, a leaf-eater raising a sharptooth is not heard of often, and while it might happen in another part of the world, the odds of Chomper finding this one in a million sharptooth kid is very low.