Yes, no need to pack any beach towels, depending on which cruiseline you are cruising on, getting towels should not be a problem. If you are cruising with Princess, your cabin attendant will drop them off the night before, you can also mention that you will be needed some. When we've been on RCCL, we pick them up at the pool deck or they will pass them out as you leave the ship. Just like AJ mentioned, be sure to bring them back with you.
I will be on the Celebrity Zenith - I take they have beach towels as well? Are they really big enough for the beach, and not just the pool? Thanks so much - leaving on Sunday and getting very excited about first cruise!
And don't worry, those beach/pool towels will be big enough for the beach. I have been known to "borrow" an extra from pool deck the eve before a beach excursion. I ALWAYS return it though. Another thing I use is an extra sarong or parero for siting on at the beach, or for keeping your bag out of the sand. It's very light weight, not bulky, dries in a second, and sand shakes right off. Very versatile piece of fabric. Wouldn't leave home w/o it!