The simple answer is yes, because Fox isn't just another network, it is one of the highest rated networks. If they want to put a fight on in MSG they will simply walk up to NY, say sanction it or we stop covering your other lame ass shit, and bam sanctioned.
Seriously though it will help. Fox has a massive amount of sway in all worlds, including political. Since Fox News has the largest audience out of all networks the last thing a politician would want to do is hold out on something small like this and risk having any mistake they make as the main headline on Fox for a week. It will barely pass, but it will pass when Fox wants to put a show on there.
First and foremost, Fox News is NOT what is considered a network in TV, it is a cable channel. A Network is one of the channels that are picked up free over the air, like ABC NBC CBS and FOX. So, while it may be the most watched Cable News Channel, it is FAR from the most watched channel.
So the next question is, what is the most watched network? CBS.
Now does this mean that FOX is not big? No, not at all, FOX is a giant. The first UFC show on FOX will bring bigger numbers than any fight they have ever had. It will get exposure to many that have never seen a UFC event before.
I think it will be GREAT for the UFC and for MMA.
Now do I think FOX will have any pull over the political types in New York in getting MMA sanction, no I dont think so.
Fox News is affiliated with FOX based soley on the same ownership. I dont see them trying to exert ANY influence over any politician because of MMA (a VERY tiny political issue), when they already have many other agendas of a much larger size!