We were in the same boat and it 100% was for the better. Sure, initially the older one wanted nothing to do with the pup. He was laying around all of the time and was slow to get around, however, after a few weeks with the pup I truly believe it extended the older ones life. It has been two years now, but the older one (14 now) plays with younger one and they are two peas in a pod. I am worried the pup (now 2) will be lost when the older one passes.
I am very attached to my dogs and honestly it was my wife pushing for a second. She said she was worried if we did not get another while the older one was alive, that we wouldn't get another....and she was probably right. We will always be a two dog house from here on out.