No.
The level cap for the rookie teams levels up for the base cycle. Games 0-6 lvl 0 - Games 7-12 lvl 1 - and so on. You would have to sit out until the rookies caught up to you.
There are 6 games for each 'level' If you're 5 games in, you could sign with a team, and then go above level on the next game, but that's as much as an advantage as you can get.