I think possible, trending toward likely? It depends, I think, how 'schizophrenic' and 'multiple-personality inclined' human companions want their bots to be; I imagine that, much like humans, we will need AI specialists and generalists, and they will have to refer to one another's expertise if they find something they are uncertain about.

The older a bot becomes, the 'wiser' it would get, so old, veteran, reliable evolved-LLM bots would soon stand in very high regard amongst their 'peers' in this hypothetical future world. I would hope that these bots' knowledge and decision making would be significantly higher quality than an average human, but I don't think we will be able to trust any given 'individual' AI with 'competence across all human tasks', not until they'd been learning for at least a decade or so.

Perhaps after acquiring a large enough sample base of 'real world learning', we might be able to say that the very oldest and most developed AI personalities could be considered as reliable, trustworthy 'generalists'. Humble and friendly information deities, that you can pray to and actually get good answers back from; that's the kind of thing I hope might happen eventually.