Dilemma/Contradiction Spoiler
In "The Time Machine" the Uber-Morlock explains how the main character's girlfriend cannot be saved, precisely because it his her death that caused him to create the time machine. This makes sense to me and is very elegant.
If Quaid's character were alive, this would mean that Caviezel would have never needed/tried to communicate with him on the radio. Ergo the whole thing would have never happened. So I would say that Quaid had to have stayed dead, otherwise the whole plot never gets off the ground.