As others have said yes it could be used for that purpose.
It is however, far from ideal.
1) it is longer and that makes it a bit more unwieldy, particular inside in tighter spaces
2) If you have it set up for hunting it is unlikely to have the things that are nice for a fighting gun to wit:
a. a mag extension. All other things equal more rounds = better in a gun fight
b. a good light set up
c. side sadle: you could use a butt cuff some will say but the way I (most people ?) run a pump makes a side saddle a better set up. I also like a source of ammo on the gun because when you grab it for that pump in the night what you have in/on the gun is typically what you've got and a shotgun is a low capacity weapon. Some will say you will not need more than what is in the tube. That is pure conjecture. Its impossible to be sure.
In sum, if you are just going to leave it in the closet. Sticking with your current set up probably isn't much of disadvantage apart from length. If you are going to learn to run a fighting shotgun then a shotgun set up for that offers notable advantages.
d. gun set up to fit the "tactical" style shooting as opposed to field shooting
Personally I am philosophically moving away from the idea that a shotgun is the best choice for HD (and I am certain that universally it is not). That said it is a good weapson system with some distinct advantages (as well as disadvantages).
If you want to use a shotgun, persoally I would suggest one set up for the task. There are common features among fighting guns but there is no one right set up. How the gun is set up is largely driven by how you will run it and various personal preferences.
Good shotguns are cheap. You can by a used wingmaster for example for $200 and a barrel for $100, or have the one on it chopped and thread for chokes. Then as you learn/decide how you will run that gun (and this is very different from field shooting operations) set it up accordingly.
As others have said if HD equals hunker behind cover and/or concealment then the existing gun is more workable
Unless you feel the need to play cop and "sweep or clear" your house, your barrel length is just fine.
I like when people have the idea that everyone lives in the same type of house as them under the same circumstances. There are plenty of legit reasons to move short of "playing cop". Say to go to a location where another family member is.