Yes, I've heard no reports of poorly fitting branded recommendations from AI models. The PR risk would be huge for labs, the propensity to leak would be high given the selection effects that pull people to these roles.
But I suspect that we're no more than one buyout away from that kind of thing.
The labs do appear to avoid paid advertising today. But actions today should not be taken as an indicator to mean that the next owner(s) won't behave completely soullessly manner in their effort to maximize profit at every possible expense.
On a long-enough timeline, it seems inevitable to me that advertising with LLM bots will become a real issue.
(I mean: I remember having an Internet experience that was basically devoid of advertising. It changed, and it will never change back.)