Yup, he's using a can. Not that it'd affect anything IRL, everyone in the neighborhood would hear that thing since 12ga is still loud as hell, but this world operates on rule of cool sometimes.
And I watched No Country For Old Men before writing this segment so I naturally had to include a suppressed shotgun.
The most detrimental factor would be weight, but for clearing a small structure, it's almost negligible. If he fired more than 500 rounds without any substantial rest periods, it'd probably lose its effectiveness, probably. I don't actually know if anyone has made any studies regarding the lifespan of 12ga suppressors.