During a competition, is there any hidden advantage to giving or receiving coffee with team members?

No hidden advantage. Just energy to play the comp.

Giving a coffee also gets you one coffees worth of energy. It also may help other team members playing in the competition allowing them to play one more screen. If your teams score is close to the next teams score your giving or getting a coffee may tip the balance of your clubs final score winning a bigger prize. This occasionally has occurred in my club. Without the coffee we would have slipped down in rank and gotten a lesser prize.