Hey guys. Not sure how much I can add to the discussion but here goes. My understanding is that experience does affect players' performances. I read somewhere that the effect is bigger when the game is on the line, but I can't guarantee that. Maybe one of the BB's can shed light on this. But again, I can't quantify how important it is and in general I don't think players care that much about it.
As for how long it takes to go up, from my sample of players (which is small) I would say it's around 1,5-2,5 seasons for a player that plays regularly (say 2/3 of the matches and reasonable minutes), a few cup and playoff games. I've never had players in the NT or U21, so maybe someone who does have can share his experience on that.