By my count, there are 23 judges on the Second Circuit bench. Their proclivities and philosophies are all over the lot. Beyond a healthy respect for hard working district court judges, and a refusal to get star struck by any party or lawyer before them, you can't assume anything.
This case would go into the hopper with all the rest of them. Beyond being reasonably attentive to matters genuinely calling for expedited resolution, nobody is getting any special treatment.
This often is a revelation to billionaires and large business entities. It is amusing to be in the room when scales drop from their eyes.
This, and people here also need to crank down the extent to which SDNY/2D Circuit judges are, or should be, intimidated by the big, bad NFL.
These are guys and gals who regularly tell entities like the US government, or ExxonMobil, to go shit in their hat. A year's revenue for the NFL (the entity) and all of its franchises combined would be a bad quarter's writeoff for ExxonMobil, and would not register as a rounding error in the United States budget (plus the US government can, like, execute people, and start wars, and stuff).