Do I need a sump with a fish less system

I cant find any info online about this and have searched quite a bit. I have a 10 gallon tank that my grandma gave me and I am thinking about turning it into a mini reef tank without fish in it. Now my question is dose anyone know what kinda filtration a fish less coral system would need, the way i figure it without fish putting nitrites in the system then I should not get nitrates or phosphates at all. I do have a miniature filter with a small floss pack filled with charcoal because I have two leather coral frags in the system and figured I would need active carbon to filter the shed's. I used water from my grandma's reef tank to skip cycling and took frags from her system, I do have a GHA breakout ATM but I think it will clear up when the levels drop from no fish. I would still need to do water changes from the corals depleting the minerals of course, but my question however is would I need a sump with cheeto at all?