I think this would be a great idea, not just to help with the tanking and buying up to not get relegated in the last few weeks issue but as another element to the game.
Fundamentally, the longer a team plays together (up until a certain point), the better their players' performance.
The multiplication factor would depend on how many weeks the player has been in the team. When the player joins the team, he has a range of -4 to -2 on his stats (similar to bad GS), then after ever week, he grows slightly until he becomes a random figure between +7 to +9 on his stats.
Perhaps, although it would make it more complex, players could have an extra stat which determines how well and how quickly they get along with their (possibly new) team.
Make sense? Sound like total nonsense? What do you think?