If your son has not had much experience, or has had problems, with spending a night away from home you will probably not want to send him for a week. A better solution might be to let him work up to a week away from home -- perhaps he could stay two or three nights with grandma or with cousins.
Many camps offer half-week overnight stays for children who are not ready for the full week. You may want to check to see if this is possible at a camp in your area. Ask also at the YMCA camp about how they handle homesick children. Children whose parents are called to come pick them up right away can get the message that they can't handle being away from home, and this can set them up for separation problems down the road.