Legate Lanius and his troopers meet General Oliver and kill him, the NCR offensive collapses, and the Legion wins.
The problem with the situation is General Oliver has allowed the Legion to have absolutely no problem widdling down their numbers in his goal to upstage Chief Hanlon. While the Fiends won't be distracting NCR, there will be the following distractions:
* Poison Gas will kill all the NCR troopers at the Strip.
* The troops at Camp Golf will be dangerously undertrained.
* Hanlon will be dramatically lowering morale with stories of the Legion's invincibility.
* The Great Khans will be throwing their hat in with the Legion.
* The White Glove Society will be serving as Caesar's Legion's new patrician class.
* Mister House won't be able to use his securitrons to beat the Legion.
* The massive casualties at Camp Searchlight.
* The spy at the airport would report all movements to the Legion.
In short, a complete disaster for NCR.
Helios and the BOS didn't really do all that much and while casualties were heavy, the forces at the Airport weren't engaging the Legion anyway. NCR would have less casualties but they're still likely to simply withdraw.