Is this position possible?

You can't create nothing from impossible...

It is surely possible

Tripled pawns on the a-file? 

Trivially possible. Black's pawn structure on the queenside can be reached by b7xa6, c7xb6xa5 and d7xc6. White has no pieces, so capture count is not an issue, and the position of the two Kings isn't a problem either.

It's possible in the context of a standard game, but it'd have to be the result of some seriously questionable play

Also the wrong position. There is supposed to be a pawn on c6.

30.b3.

forgot, fixed

In a standard game? Not likely, but I suppose it's theoretically possible.

Is this position in a puzzle? 

I doubt it, as it seems a win to White no matter whose move it is.