He can't ring in before Trebek has finished reading the answer. The system is locked until that point. He can get good at timing it so he anticipates when it will be unlocked, but he then is still competing against the others at that point. Before a contestant is on the show, he/she has been through practice rounds learning how that works.
As far as costing them money, he is making them a fortune. Ratings are up something like 35%. He is money in the bank for them. He makes 50G a show, Ray Romano makes close to 2 million a show. 50g is nothing in TV land.
dago