Another good thing to monitor could be how many of demoted teams returns back next year and/or within two years i.e. the other side of the change. Because as Crazy Eye mentioned Div 1 teams don't see many new faces. Similar situation fro lower levels depending on how big particualt country is, how long the country exist in BB and how dense competiton pyramid has been created.
Certainly you will agree that being in the top division for two seasons is probably enough to equalize out any advantage being there before gives.
It depends on conference.
First things first - diclaimer: you can see how i am doing so i should clarify I'm not complaining; I have got there pretty early after playing 4 real seasons naturally not having a team as well builded as others, older teams have;I got unlucky and became the only rookie team in a tougher conference, where the rest 7 teams would be all top 10 in my country (including BBB finalist) - so be it, those things happen.
Now to the nitty gritty. To equalize? With good management and bit of a luck maybe. Any advantage? I doubt that. The period needed to catch up with other teams on the next level is becoming naturally longer - i.e. it is different to get into Div 1 the second or third year of its existence or now. There are of course teams you can catch up with quite easier and then there are powerhouses. Catch up with them won't be any easy, depending on country specifics it could be managable to quite impossible. In Div 1 you usually have not only better rosters but better managing managers too and that is the difference. I guess you meant average team of that divison - I can't tell yet. One big factor is how ready you were to promote - whether you were a clear winner of your league, a dominating hegemon or just oen of the bunch of above average teams or a dark horse. Injuries to key players, running into good team in rebulding mode and other events are often big factors and luck is usually involved. In addition play off engiune can be pretty random as I learned in my very first play offs. All I can say is that although I stayed in Div 2 3 seasons (from promotion to promotion) that such a scenario is not widely typical and I got lucky, took my chance albeit there were teams with better rosters on paper (when healthy).
I think that the question of how long a newly promoted team needs to catch up to become ... (slightly above average?) would be an interesting topic for a discussion - at least from the how-users-perceive-that point of view.