Yes, hypothetically, you could give a three year old a shower. Unfortunately, your child could be like my son, who absolutely would go ballistic if we tried to bathe him in a shower, and wouldn't even go into the aquatic building at our local zoo, because it had a waterfall that sounded like a shower.
When my son was young, we also were "upgraded" to a HA room at All-Star sports. It had a king size bed, a small refrigerator, and faced the pool. It also had one of the funky showers. Fortunately, we were able to sweet talk my sone with much cajoling to take a shower. Thereafter, he was able to take showers, he was about 6 at the time. We were OK with the king bed, because he just slept between us at the time while we were on vacation, but, technically, I don't think a family of three should have been placed in the HA room with only one bed.