Yes, you can do what your planning but its not ideal.
Live rock, carbon, GFO and a good skimmer (remora will work fine on a small tank if it will fit) would be my suggestion. If you want to make it simpler, you can use something like Chemipure Elite in place of separate carbon and GFO.
Dry rock can be used which will eventually turn live if you want to save $. The rock will provide all the biological filtration you need.