My reason that they will win is this.
A. The battle for the Dam itself will be harder than you think
Dispite the Legion coming in from the sewer pipes, Oliver is already sending massive numbers of troops to the Dam. Hell even House himself said Oliver has funnel vision. That said many of the Legion's top troops will die.
B. The artilley will stop a reinforce
The only way they'd have enough force to refortify the Dam and then move on. That said artilley will ensure that's not going to happen.
C. So Forlon will stand
There's no way a few rag tag troops from Nelson will be able to mount a large enough attack to destroy Forlon. Hell like I've said before one NCR sniper could take out the whole place.
D. Nelson won't get more troops
THe fact the Legion held Nelson is a miracle within itself. And looking at the Colorado there is no way the Legion could take Forlon without having a massive number of troops left.
E. Forlon troops will take back the Dam
With the Legion weaken, elite troops killed, and Camp artilley bombed, they'd be in a bad situation and the Dam would be retaken within a day or two.
Good morning man. Here's my reply
A. Everything that's implied by dialogue between Caesar and NCR troops is that the NCR is at the disadvantage during the battle. Oliver is taken by surprised during the battle by the Legion's tactics and the only thing that stops the soldiers coming from under the reactor is the Courier. That said many Legionaires will die for sure, but I do think that you're either ignoring the advantages the Legion has or you're overestimating what the troopers can do. Either way let's move because I think we both agree that the dam will be lost to the Legion.
B. I know you've mentioned the artillery before and I've ignored it for one reason: I've never heard anything about this artillery. Maybe I've missed something, and if I have let me know where it's mentioned+found, but not once in any of my playthroughs have the Legion or the NCR or anyone else mentioned artillery as a deciding factor of either side during the fight. I think you're using speculation here, equal to saying that "Oh the NCR will win because they have bigger guns" or something. Though again, if I missed some dialogue or a quest dealing with the artillery let me know.
C. Now assuming that the Legion will take the dam, there is no way in hell that the NCR will be able to hold Forlorn against assaulting forces from BOTH the dam and Nelson. As I've stated before the game makes the dire situation of the camp infinitely clear. Every quest in the camp deals with getting the Courier to compensate for lack of supplies or lack of troops, talking to the NPCs in the camp will reveal the poor morale and the sad state of things, the letters found around the Camp reveal the plummeting morale and lack of supplies further, Mr New Vegas talks about how [censored] Forlorn Hope is every. I believe that these facts, and they are facts, should be taken into more consideration than whether someone thinks one sniper would be able to take out a lot of troops.
D. Again, Forlorn Hope is not in any position to defend itself from a moderate force, let alone from the remaining Legion from the dam and the Legion around the area, from the Cove and Nelson.
E. Again, Forlorn Hope cannot is not in that position and to assert that the garrison of the camp could retake the dam from the Legion and Legate Lanius is crazy.