I can't see him not reporting the death, I actually think if her health takes a bad turn and she doesn't like just have a stroke or something she'll probably pass away in a hospital. I can't see him not trying to take her to a doctor if she gets sick or has some kinda nasty accident, Barb is getting to that age where a fall can be a pretty serious event. So unless it's a sudden thing he's probably going to get someone else involved to help.
The funeral arrangements are a different story, I doubt he'll be able to navigate that mess on his own, I know from experience its not easy even if you are of sound health and mind to begin with. Losing a close loved one, much less a parent fucks everyone up. I imagine as long as Barb has some time before she actually goes she'll get the ball rolling and it'll be the funeral home themselves helping Chris through the process, even with as fucked up as Chris is if there's anyone with enough patience to help him it's a funeral home. Especially if Barb can at least get Chris started on the process. Paying for it and how much it will cost will be the real problem.
Plus he'll probably develop some unhealthy coping mechanisms or go on a spending spree to try and cheer himself up.
