Indeed it does. Now, we not only have five (or 7, if we include your younger children?) who need supervision, but one of the supervising adults is tired as heck. More eyes on the kids would be even better in this situation.
But based on your stated expectations, if I were a parent I would receive this invitation for my son and say to myself, "well only HE is invited, clearly, so I can't come. It's a pool party, so that doesn't make me entirely comfortable, okay, he CAN'T go."
Presumably these are his good friends? You'd be okay with parents saying no to your party? You might get only one mother out of four comfortable in this situation, just leaving her child to be watched by others in the pool. (especially if one of the supervisors is a teen herself)
Or, my other option is to ask you, "is it okay if I come to keep an eye on things?" (thus making a pest of myself and someone who had to be "fed")
Or ignore my instincts and send my son anyway, because he didn't want to disappoint his friend on his birthday?
Three bad options, it seems!