No, after the main quest is finished and the ending screens and narration play, the game is over. You can go back to your last save and continue on with any side quests that you had left unfinished, or go explore the rest of the wasteland, and when you're ready, you can finish the main quest and end your game again.
This is true, and this was revealed even before the game was released, though of course, if you weren't following the development of the game, you may not have known this before hand, but now you do know. I'm not going to debate whether this design choice is a bad or good thing, because I'm sure there's already a thread on that subject, but unless New Vegas gets a DLC similar to Broken Steel for Fallout 3, which I don't really expect to happen for reasons that I don't feel like elaborating on right now, or you get a mod that allows free play after the main quest, which, obviously, is only possible if you have the PC version, the game will end once you finish the main story. So if you want to keep playing, you have to either load a save from before the point of no return, or start a new game, either way, now that you know what happens when you finish the main quest, you should keep this in mind, and finish any side quests you want to complete with your character BEFORE getting to the point of no return.
Though I will say I learned something from this thread, and that's that I have no reason to care about the reward for completing the game on hardcoe, if I ever decide to play hardcoe mode, it will be to experience the differences it makes to gameplay, not to get whatever reward is offered, which is how it should be anyway, the reward is just there to discourage players from turning off hardcoe mode the moment things start to get difficult for them.