Not as long as one might think. At least not for the actual penguin, that unfortunately was plunked to extinction for nice down bedding, and not the impostors from down south.

(Partially joking here. But the great auk was called penguin before antarctic penguins were first described, and although auks and modern penguins look similar in some regards, they aren't very closely related.)

Certain death indeed

No wonder it dies

So there's nothing wrong with taking this dying penguin and raising it as a pet?

or worse, it could introduce unfit behavioral factors into the gene pool

As long as the penguins haven't discovered warp drive, that is.