Update #1 - 14:31 UTC: Rockstar have now put up an official FAQ for BattlEye where they state:
Is BattlEye compatible with Steam Deck?
Steam Deck does not support BattlEye for GTA Online. You will be able to play GTAV Story Mode but unable to play GTA Online.
Note: GTAV and GTA Online are not officially supported on Steam Deck and all technical support questions should be directed to Valve’s Steam Deck support content and community.
I’m still currently waiting for an official statement from Rockstar on any plans to enable it, since BattlEye as mentioned below is supported on Linux / Steam Deck.