Not really. They only provided the ability for CoD because ATVI wanted it to make more money from the entire userbase across all platforms.
If ATVI becomes Microsoft owned - working against PlayStation's interests by trying to migrate users, they have every right to withdraw the feature.
The irony would be that CoD would likely grow and generate more money on PlayStation in Microsoft ownership than it could have in ATVI ownership, and kill CoD on xbox, so it is very much a strategy I expect them to enact if the CMA fail to block the deal.
Why do you think there would be a backlash and from who? This is exactly the type of reason why this deal should be blocked IMO, because it is bad enough that an essential input could go first party, but to then foist self-harm constraints on PlayStation like having to keep cross-play - hampering their ability to compete/survive such a big move by a $2T company - would be even worse for competition IMO.
edit:
Killing cross play would also mitigate any damage from gamepass to PlayStation B2P CoD revenues , because despite the cheaper entry price to play, the main userbase would be locked off on another platform.