As with most things, the answer is going to be a big 'It Depends'.
If the queen is accepted then fine. but it things are to far out of whack, she will be rejected and killed outright by the bees themselves, and they will then raise their own queen. I'd always start her in a cage so they cannot kill her, frankly, but that still isn't a guarantee. and you also still do not know what the new queen will offer either. but they have attempted to put regular queens into say a AHB hive...and they just slaughter her and requeen themselves.
but if she is accepted, then in 6-7 weeks it's going to be pretty much her DNA in the hive, and then you still have to go by the nature vs nurture aspect...ie if the hive has a lot of robbing, or aggression towards it, is in a bad location with a branch beating up against it in the wind, maybe, then they will come out how they come out, I suppose.