You could use that combo provided you only use the 20 gauge for deer hunting. The regulation does not prohibit possession of a lesser caliber, only the use of it. Unlike archery hunting which completely prohibits possession of a firearm while hunting. I've had other people ask if they could carry a .22 rifle in addition to a shotgun and there's no issue with that. Again...just don't shoot a deer with the .22.

26-86a-4. Firearms and ammunition
(a) During the open regulated shotgun season, deer may only be hunted with 12, 16, or 20 gauge smooth or rifled bore shotgun using ammunition loaded with a single projectile. Shotguns used to hunt deer shall not be capable of holding more than three shells and shall have its magazine plugged with a one-piece filler, incapable of removal without disassembling the gun, so its total capacity does not exceed three shells. (b) No person shall possess a capped percussion lock firearm or a flintlock firearm having powder in the pan, where a loaded firearm is prohibited.