It may, or may not, depending on what the BG is wearing, how thick his or her fat layers are, their muscle layers, and the angle you're shooting.
With a shotgun, I'd stick with buckshot or slugs. A handgun would have monolithic or bonded ammo (for the same fat and muscle and bone issue), and my rifle ammo for HD is something that penetrates at least 8-15".
Nostler ballistic tip is good ammo also for HD, because it has fragmentation properties, but also holds enough of the bullet together to penetrate through your BG (having less energy on the other side of his/her body). I also have a mag of 125 grain .308 next to the hornady 110.
An advantage of using the AK is the folding stock option, which could help maneuverability in the home, though in a HD scenario, unless I'm moving to children, I'm going to stay put and use the tactical advantage of the doorway.