cf - Sorry to read about your son. It really stinks to get sick when away from home, and feels even worse when it seems like so much is on the line.
I'm gonna share a story, not to worry you, but to add a little more data to the question. It just gives a little(?) insight into how coaches think sometimes. Even with the story I'm gonna tell you, I do believe if your son can play at the school hosting the camp, they will figure it out and not let his illness or performance while he was ill dissuade them from recruiting him.
Anyways, here goes...
Older son was a senior at Stanford and the Saturday starting pitcher. They were at Texas for a 3-game series (Friday, Saturday, Sunday). On Friday when we got to the game, he was nowhere to be seen in the dugout. I asked one of his teammates before the game where our son was...'throwing his guts up in the locker room, he's really sick!' A little later he did pop his head up out of the locker room...in and out throughout the game.
That night, we usually went out to dinner. He couldn't make it, no way. But I did ask him if he'd be able to pitch the next day and he told me, 'Yes, <pitching coach> said that there may come a time later in the year when we're pushing towards Omaha and we need you to start and carry this team that day...even if you're sick, so you might as well learn how to do this and gut it out now.'
Despite not having eaten in a day and a half, he did start the next day...went 5+ innings and left the game with the lead...which they eventually won. He could still barely eat that night.
Later that year they were in Omaha playing in the College World Series.
This situation is not the same as your son's and the fact that your son was ill is not very likely to affect that school recruiting your son. But once he's there, playing through injury, stiffness and illness will be expected from time to time.
Best of luck and I hope it works out for him!