I would say yes... I don't do much camping by the lakes but Elephant butte is just north of Caballo lake. there is a small RV park in Caballo also.
Palomas Gap is the typically why out but it was reported to be washed out last summer and it's a very narrow shelf road. We were going to see if it was but with the braking problems we didn't... I'm actually glad we enjoyed following the GPS out to the east/north