My oldest attended one the summer after 4th grade. It was a program for kids entering 4th-6th. She liked it but it was very expensive and we can't swing the cost at this point to do the ones she'd really love like Duke's Marine Lab, although she, too, has qualifying scores from this year and last.
My take on it was that I'd be surprised if they'd let you do it as a day camp, but it can't hurt to ask. Dd didn't find a huge amount of bonding with the other kids although she liked them well enough. I do think that the evening activities and meetings w/ other kids in the residence halls are probably an important part of the bonding aspect if that is what you're going for, though. I don't know if just going for the academic stuff during the day would be enough to really get to know the other kids especially if the rest of them are playing cards in the dorms at night and having time to just hang out.
If the alternative is not going at all, though, I might check into the day camp alternative if my dc was really interested in the program. The one caveat to that was that my dd is seriously interested in marine mammology and found that taking a class in marine biology was a poor choice b/c she didn't feel like she learned much since it was probably geared toward kids without as much background knowledge.
