Personally, I'm partial to the view presented in the video; that is to say, the Legion may win New Vegas, but they won't be able to conquer the entire NCR in the long run.
However, I don't think that necessarily spells the end of it. Assuming the best possible outcome (i.e. the Boomers on their side, Caesar survives the tumor and their enemies eliminated) Caesar would now be in control of his new Rome and would likely implement the societal changes he intended to once he held a major city in his territory. House's technologies would be in his grasp and although he wouldn't be able to unlock the MK II upgrade, he'd still have an army of securitrons on his side he'd be an idiot not to utilize, as well as several non-combative technologies such as the irrigation and power systems.
It still wouldn't be enough to conquer the NCR, but it would help and perhaps even definitely establish the Legion as a stable nation; assuming Caesar picked his own successor before his death and did so wisely, Lanius would cease being a problem entirely.