If your round trip includes landing on the moon, not even close. Otherwise yes. The current vehicles would also be capable of putting a theoretical third party lander on the moon that could return, but not one is developing such a lander (and it would be fairly weight constrained, ~2/3rds the mass of Apollo).
The really exciting thing for the moon/mars isn't what SpaceX has already has finished hardware doing though (lowering launch costs by, optimistically, an order of magnitude), but what they are actively in the process of doing. Developing a ship and rocket that they claim will be able to put on the order of 100 tons on the moon... lowering launch costs by multiple orders of magnitude.
Given their track record, the money they are (visibly) spending on this goal, and the fact that what they say they are going to do seems possible, it is reasonable to think that there is a good chance they will succeed.