Does Andrew Ryan survive the events of BioShock?

You're thinking a bit too much into it. There's a Vita-Chamber in Ryan's office, however...

It is disabled. Ryan turned it off. He chose, he did not obey.

I would give you a screenshot, but my Bioshock savefiles are long gone.

Ryan didn't need to run away. He didn't want to. Rapture was his life. and by that time...

He had set in motion its destruction, by himself. He would rather die with his city than letting what was left of it to be in the hands of Atlas; who he probably suspected to be Fontaine, but we have no confirmation about it. Moreover he wanted his city to die with him. Because he was rapture, and rapture was him.

In regards to Bioshock 2. The little sister reviving subject Delta is pretty special. She rigged one Vita-chamber to work outside of it's parameters. The chambers were only for Ryan and his DNA. And they were not intended to work years later. But again, we're talking about someone special.

Besides that. No, Ryan's does not show up in Bioshock 2.

Or ever again for that matter. He is dead.