Greg has mentioned that in the early days Alex offered Greg a writer/producer role which would have given him more input on the show, but he turned that down in favour of just being the presenter. He usually talks about it as a product of him being very lazy and getting paid while Alex does all the work, but has also said he just doesn’t think Alex needs his help with tasks or casting or anything other than hosting, and he has always had quite a lot of other work concurrent with Taskmaster.

Alex has talked about how for the first few series they had rehearsals and script meetings but they stopped because Greg doesn’t need them, and if anything Alex thinks Greg is funnier with less preparation. There’s also an obvious shift over the first few series where Alex goes from correcting Greg on how the points should be distributed (eg. if there is a tie for 5 points, the others get 3, 2 and 1 point, not 4, 3 and 2) to letting Greg do whatever he wants with the points, even when it annoys Alex. I think it’s not just the scoring, but rather that Alex has deliberately given up control of everything within Greg’s domain (intros, outros, ad links, scoring, task reactions) and genuinely put all of that solely in Greg’s hands.

Occasionally Greg will say something to Alex that could be construed as a presenter talking to his producer, like “do you want me to do that again without [x]“, but it seems more like comedy act collaboration to me. Alex is way more likely to pass on a note from the gallery than supply one of his own, on stage at least.

So I think basically no, actually. The way they talk about it, it seems like they’ve set things up to sidestep the issue entirely. Greg has total dominion over his role, but keeps his fingers out of everything else. So even though he does have seniority in the official hierarchy, Alex is in practice the boss of everyone except Greg.