No that wouldnt happen. NCR obviously have Rangers so there's no way the legion could win. Who cares how spread they are. They still beat the hell out of them.
The rangers are an effective force if used well. Oliver won't use them well.
He makes his plan pretty obvious from the get go. In order to overshadow the tactical expertise of his predecessor who, despite using seriously intelligent tactics still almost lost out, succeeded in gaining glory for his victory.
Oliver wants to march his men onto the dam, kill the legion as they try to take it then push through to their camps and kick them out. Sound plan if you outclass your opponent by several degrees and the dam is a defensible position.
They don't and it's not.
Firstly, the legion is behind them, they've got men around the place and even have a couple of permanent settlements (Nelson/Cottonwood) where they can raid from and the NCR can't do a thing about.
Secondly the dam is not defensible, it could be and it should be but Oliver's lack of interest in reinforcing it against attack leads to a serious problem, as is shown during the CL playthrough Lanius knows of tunnels which can be used to infiltrate the dam, he uses them. Oliver doesn't even know they exist.
As for the military superiority, well, if we take tactics out of it and made it a straight slug I'd say it's pretty tight, despite the lack of reinforcement since the last battle (where CL have rapidly grown in power in the region) what they have got is the rangers, a highly effective fighting force, expert skirmishers outfitted with night vision and powerful weapons. In an extended fight they'd make the difference. In a straight slog it's tough, but CL has got more moral, they're not going to run, they want to kill the NCR scum, the NCR are afraid, the troops are people who want to go home, who don't like it in the Mojave, who want to make a difference perhaps, but not by giving their life.
Throw in the tactics and the Legion wins outright. Surrounded, hit on all sides and given a simple escape option. The NCR would be kicked out and fast. Graham was tactically weak, Lanius is not, for all his bloodthirst he's astute, he understands his enemy and does not underestimate them.
Ok, I believe NCR is better because people often thrive more under the republic rather than a dictatorship. There are many Intelligent officers like colonel Hsu and Moore. Despite being hit by legion patrols daily they still manage too stay strong even though they're poorly supplied. Veteran Rangers are not overpowered as much as they're amazIngly skilled, the best of the best. My first playthrough with the NCR I thought at he Hoover dam, oooh a bunch of rangers that are going to die in a second and then I'll feel bad! But no they [censored] any centurion that was in they're way haha. Those are my points.
Hsu is smart, Moore is...ok. Oliver leads them though. With Oliver there they must defer to him, such is military command. Oliver is an imbecile. Seriously, he's just an idiot, through and through. Even with Hsu in charge it would be tough as hell (though, we could argue if Hsu was in charge for some time things would improve). With Oliver it's a no brainer. The toughness of the rangers is bizarrely exaggarated in game, but even if we take their strength in game as canon they'd still lose out. The legion has them so screwed over it's unreal.
Without the Courier's intervention, the fight's over before it begins. Oliver floods the dam, the Legion encircles them and cuts them down, slowly. Maybe leaving them the funnel through Boulder City, likely not. The NCR on the dam would probably be killed to a man. McCarren would either fall to the Fiends or be hit hard enough that reinforcements couldn't come. Bitter Springs is in no way to give aid even if the Legion don't destroy it beforehand (assuming Boone's quests raiding party would exist without the Courier/Boone). The embassy on the strip would be cut out of aiding McCarren thanks to a certain traitor and would be too far to reach the dam before it was lost, even if they did they'd be harassed en route by forces from Bitter Springs, not to mention the fiends...
Novac falls to Cottonwood, presumably, while Forlorn Hope has no chance of survival against the Legion from Nelson (seriously, they'd be screwed). Golf would survive to give aid but Hanlon would likely go down fighting, his rangers with him. No doubt most of the others would flee or be killed.
They'd be pushed back to the Mojave outpost and fast. There they'd likely be hit with small probing attacks while the Legion fortified and advanced, engulfing the Mojave. Once strong enough, they'd take the outpost, making it their forward post of operations into NCR land.