Does the team Captain do anything for the overall team ratings or is it just a way to upgrade those players only?
Team Captain contributes to your team OVR if you have him in a starting position, i.e. FB1, HB1, CB1-3 or WR1-3.
OVR doesn't matter though so don't get too hung up on your team OVR and feel free to experiment with playing players OOP even if their OVR lowers as long as you don't need their team chem in that spot.