I suppose after you first determine whether it "glows in the dark" to give your position away, you could practice with it at night when it is completely dark and run through your strategy for how you would use it. As you practice (with your NON-chambered gun in hand, not just with the night-vision device), you may discover possible pros and cons to your technique and how comfortable you feel about it.
Do you have a handgun to use instead of a shotgun? Seems that if you are going to have something in each hand it would be preferable to be able to use your weapon quickly and with only one hand, if necessary.
There is also the additional issue (widely debated of course) of you turning corners to clear your house with a long gun, which is much less compact and cannot be held as closely to you. Furthermore, with only one hand on it, it would be even easier for it to be taken from you...but I should probably not be opening up that can of worms and taking us off topic