Not really. Especially since the league itself was willing to let Elliott play back in week 1 due to the late timing of their announcement. I think they're argument comes down to respect for the commissioner's pronouncements given the obvious latitude the CBA grants him, but it's unclear how the league can make a case that they're hurt by justice getting delayed. Especially not on a balance of equity basis, since Elliott stands to lose so much more in terms or records, guarantees, post season opportunity, and endorsements.
The league probably makes a broad appeal to the public interest argument, that it hurts interest in the league to be getting so much negative publicity in a situation where they have perfect authority to suspend a player. At a time when viewership is trending down to begin with. It's costing them in terms of their reputation with potential advertisers, or that the appearance that they can't enforce a DV suspension might counter their attempts to court an audience who'd be favorable to an announcement of a DV suspension. But it's pretty tough to put a convincing measure on what that harm might be worth our how it could be tied to this case.
I think the league's strongest argument is on the 'likelihood of success' challenge.
