It's more the rat piss and droppings I'd be worried about. Nevermind the rat
Had a squirrel in mine once. Cleaned it out, let it burn for a while, good as new.
I'd be more concerned with the fact that you have rats.
You have 2 options....
1. Man up, clean the grill and enjoy your steaks.
2. Buy a new grill and BBQ tomorrow
Considering rats carry diseases, I'd take option 2 and not risk it.