Can I erase my phone and still have my apple watch work with cellular?

I had to send in my iphone for repairs, and once they told me that the wait could be between two weeks and a month, I decided to get an apple watch series 3 to hold me over. Well, I bought an iphone SE for the mean time to set up the watch, and since I'm not interested in keeping the phone, I was wondering if I could erase the phone and return it and still have the watch be functional for calls and texts via cellular since it's already linked to my phone number. Is this possible? I would really like to return the phone now and not have to worry about it.

Thanks!