Hi Lisa is right you see a lot of different cover ups. One thing I did notice that all the ladies in the Horizon court did have them on. Where on other cruises some people did not wear coverups when they went to eat. There are so many different ones to choose from, probably now on sale because the stores are showing school clothes.
It wouldn't be inappropriate. However, unless you are really cold natured you will probably be hot and uncomfortable wearing the robe during the day. It is perfect to take to the hot tub at night though.
If this is your first cruise, you will also find out that you don't just go to the pool and back to your room to change afterward. You will find that if you like to sunbathe or swim you may want to have your swim suit on most of the day so comfortable sun dresses, cover ups, T-shirts, shorts, etc are easier to lug around than wearing a big bulky robe and they will dry very quickly if you get in the pool and put them back on while your suit is a little damp.