I highly doubt it. They wear the same clothes. Maybe he survived and the hat and jacket are 200+ year hand-me-downs and the Mysterious Stranger is his great(x4) grandson or something.
You will also notice that the color scheme is slightly off and his tie is a totally different color.

I don't think so.

I don't think the Mysterious Stranger is the Vault-Tec employee from when you start the video game for the first time. If you look at the Vault-Tec employee guys face and at the Mysterious Strangers face they do not look the same. Also I do not think being cryogenically frozen or put into stasis for 200 years that your face will change that much. Or maybe both of their faces look the same and I just can't see it due to my vision degrading a lot over the decades passing by, but I just thought of this, what if the Mysterious Stranger is Shawn the baby instead? It likely is not Shawn though.

In the announcement trailer they had a guy walking under a street light in a city, and he was wearing what the mysterious stranger wears. I was assuming they we alluding to him being the stranger.

he is totally the mysterious stranger, turns out vault tech is actually really serious about keeping it's people alive (even if it is for more insane experiments)

I really doubt that Vault Tech Employee (Let's call him Roger) is the Mysterious Stranger. I have noticed a lot of people alluding to this or flat out asking. Like I said, it's doubtful at best.

It may very well be an intentional Easter Egg/nod to the Mysterious Stranger.

I doubt it's literally him, though, heh.