Rex doesn't get much in terms of character development, that's true. It's also kinda sad that you have to kill another dog if you want him to be happy and complete his companion quest.
There's also Roxie in Old World Blues. Sure, even less significance than Rex and easily missed, but she's still there. Her ending even says she creates cyberpuppies with Rex. Maybe those will appear in a future Fallout.
I'm not sure how much of New Vegas is in Bethesda's canon though. Heck, I'm not even sure if the Fallout 3 DLCs are all canon. Mothership Zeta would give some interesting stories to hear.
Then again, even if they may be canon, as I said before, we don't know WHEN Fallout 4 takes place. It could be before or during FO3/NV. "200 years after the War" is quite vague, especially since '200 years' could mean 180 or 220 easily.
By the way, if the PC survives by hibernation, but then why didn't House use the same technology for example? Tranquility Lane in FO3 has seemingly 200 year old people trapped in the sim, who don't seem to age, so House could also stay connected to his computers. And it seems RobCo had pretty close ties with Vault-Tec. Maybe Braun was simply keeping hush-hush about Vault 87's stuff.
If it's not hibernation, then what? IIRC, Androids are post-war tech, but based on the OWB Think Tank, a brain can be preserved quite well in a cyborg body for 200 years. Rex' brain didn't do so well, but maybe Vault-Tec had special machinery.
Still, being a cyborg is a no-go. It would mean poison immunity and probably rad immunity too. Not to mention endurance that's way too high... actually, that's all plausible, seeing as how much stronger the PC is than your average soldier in the Fallout games.