I agree with psycho. Actually last year we had a situation where the AD wanted to limit the number who went (after we had always taken everyone in the past). This was sprung on us at the last minute. Using exactly that argument, we were allowed to take all 16 guys. They practiced just like normal right up until meet day.
If we had a team the size of St. X or something, I'm sure it wouldn't fly to take everyone overnight and that would be a supervison nightmare, but certainly the school would bus the non-running kids down on Saturday.
Even when we just qualify individuals, nearly everyone on the team goes to support them on meet day. This year with 2 guys and a girls' team, I think we only had 3-4 HS kids (out of 28) not make the trip in one way or another. We had several of our JH kids make the trip too. It's an invaluable experience for the non-running kids.