Yes. They do rent chairs and umbrellas too if you'd like. We had to reserve the night before or they were sold out. It's not crowded though; it's great!
If I remember well you are provided with beach towels in your room which you can exchange as often as you like at the pool. Now I might be mixing up with Hilton Head concerning towels in your room, but for sure you can get new towels at the pool. The pool can be noisy during the day, best time of the day to enjoy a quiet time at the pool is early morning. There is no quiet pool option (something we enjoy so much at Old Key West).
That is how it was when we stayed there last too. Your beach towels are in your room. They are bigger and a different color than your bath towels. You take it to the pool. You can go to the window and exchange it for a new towel. I thought it was a little strange, but it seems to work. If you exchange two you get two back. We had 4 in our studio and there were two of us so we had backups.
Towels are in room one for each person the room can accommodate. We had a 2 bedroom lock off so the one room had 5 towels and there were 4 in the studio. So, we got 9 fluffy big towels for beach and pool. We would exchange them each time off the beach so we always had fresh towels.
We were there in August, umbrellas and chairs were not a problem on the beach. But I did rent them for 3 consecutive days because I wanted a certain spot.