Chance to get a stay of the preliminary injunction are slim and none for NFL..........no legal argument can be given as to how Zeke playing now and serving the suspension later, ala Brady, would do irreparable harm to the league and that is the standard they would have to show at the 5th Circuit.
Their motion for a stay will be denied..........best they can hope for is that 5th Circuit agrees to an expedited appeal process, but that would still take months. The average time from motion to decision in 5th Circuit is just over 8 months, so even if you cut that in half you are looking at mid January at the earliest.
Also keep in mind that the 5th Circuit overturn rate is just over 7%, meaning 93% of the cases are upheld. So its not going to be a cake walk for the NFL to get a reversal from the 5th, they really don't like overruling their lower court judges.