A Halo Battle Royale would be excellent for the game's population. CoD Modern Warfare has Warzone but still manages to pull in plenty of people for its other gametypes as well. While you wouldn't want an oversaturation of playlists, I don't think that'll be a problem. If they use the MCC's playlist features and include a customs browser I doubt that Infinite will be hurting for players.
They denied a battle royale mode for Infinite three times.
To be specific, the Franchise Writer denied it once in 2018 with that BR pun, stating they weren't interested.
In 2019 though a "Microsoft Insider" Brad Sams said it was being considered. Frankie would later say there is no plans for a Battle Royale at launch and that they wouldn't discuss content until they were "ready".
After the delay in 2020, the Community Director Brian Jarrad said rumors were, "Unfounded".
It's not likely the game will launch with a BR mode with all that considered, but their language is pretty non comital. I'd bet we'll see BR happen eventually, even if after launch. It's a major potential draw for new players that Halo could use well considering its large sandbox. 343's attempt for monetization via skins and Free to Play multiplayer also smells of BR, but that's moreso just by association.