I agree with the others. When I was still very young, maybe 5 or 6, we brought home a kitten who proceeded to torment our older cat. The older cat wasn't ancient, but had been showing her age. We didn't know it at the time, but she was also about to become very, very ill, and while we loved the kitten, we always regretted that our older cat couldn't have had her last few months be peaceful, calm, and low-stress. The illness that killed her would've done so with or without the kitten in the picture, but that doesn't mean it was ideal for her to have to put up with an obnoxious, high-energy youngster while she was deteriorating.
I know my anecdote isn't about dogs, but I think they're comparable. The only way I'd bring a baby puppy into a home with an elderly dog that's deteriorating is if I was sure I could keep them separate most of the time while still giving both as much human attention and interaction as they need (and puppies need a LOT of both). Really difficult, especially if you're only a one or two person household or have a smaller living space.