The exact correct answer is yes....or no....Either scenario works just fine. I doubt you are going to keep much debris out since there won't be a lot of debris where your hose is stored.
If you like to connect the ends, feel free. If you don't feel like connecting the ends you will do no harm. In the last 20 years of full timing I have never connected the ends and I am still doing pretty well. However, that still does not mean that not connecting is the right answer. Only you have the right answer as it's simply a personal preference thing.