Hey Paws!
When a cat loses a sibling or a buddy, they will have a period of mourning but they are very specifically mourning for THAT particular cat, and we sometimes see that people are too quick to replace a lost pet, as they assume one will be welcomed with open paws by the resident cat!
I would ask how old is Paws now? If he's elderly, and set in a routine which you feel would be easily upset, then I would hang fire and see how he goes. Having said that, most good rescue centres get to know their cats very well, and it is often just finding the right cat, for the right situation.
If he has shown in the past, aggression to other cats it might not be a wise move, but most cats settle with time, (although of course there are the inevitable cases that don't work out). I would perhaps ring the rescue where he came from and find out a little more about his past and what his experiences have been, and also maybe see if you can foster a cat you might like to take on for a trial period (this isn't always possible as pen space is so precious!)
Also, does he have a catflap so that he can come and go when you're not there? If he has access freely to the outside world, it's unlikely he'll get bored, especially with the summer months coming up where he can lounge and play in the garden.
Hope that helps!