I doubt it because the issue the NFLPA is arguing has to do with fundamental fairness during arbitration and the arbitrator's authority to compel/exclude witness testimony.
However, please note, the 3-person panel assigned to next week's hearing is only deciding on the injunction, not the merits of the case itself. Assuming Chin is on it, he could (theoretically) set aside his opinion on the merits of the case and give Elliott an injunction based on the notion of irreparable harm. (I wouldn't bet on it, but it certainly is possible)
Manzant is a Texas judge in the 5th District and his opinion will have no bearing on the 2nd Circuit Court of Appeals. Not only is the Cort of Appeals a higher court, but it is a different district.
IMHO the biggest deal is the denial of having Elliott be able to confront his accuser.
IMHO a proper arbitrator would have allowed Elliott the chance to confront and cross examine his accuser. And if she refused to show up then there is no compelling evidence of guilt and he should have overturned the suspension. Granted, there's no compelling evidence of guilt anyway but an arbitrator should go with the testimony before him/her, not news reports or hearsay.
I do not believe she spoke to that point in her ruling (I am not 100% sure of that, but I remember her addressing the point of failure to compel testimony)