I believe you are right cyanight. If the Brits sent planes there, that would create a hostile sea zone and the German fighter could scramble. Then, assuming a UK win, the UK troops could leave the US transports and land.
If the German fighter wins the battle, I think the UK troops would simply stay on the transports. Still nothing would happen to the US transports.
I guess you could say that the German fighter is patrolling up and down the beach, keeping the UK troops from landing. Of course, in real life, why wouldn’t the German fighter go out and blast the undefended US transports, right? Well, that’s the rules we live with.