I'm not entirely sure that RAW allow you to use Polymorph Any Object to turn something into an Undead creature (it "functions like greater polymorph", which is limited to living creatures).
But, that's a boring answer (and one I'd be unlikely to enforce as a GM), so let's assume that Undead can be created via Polymorph Any Object. I'm pretty sure that the creature would still have a Con of -.
First, Pathfinder's Polymorph base rules says nothing about Polymorph spells actually changing the type of the subject. Thus, the creature would still be an Undead, and would thus still have a Con of -.
However, that means that, technically, you could polymorph a wooden box into a human and it's type would still be "object". This is silly, so let's assume that PAO changes type and not just physical appearance. In this case, the result is an Undead creature. Undead still have a Con of -, so the resulting creature would, too.
One could imagine that, during the second or two during which the magic is doing its work, the target's body starts working again, so it might have a Con of 10 for a brief moment, but that leads to all kinds of weird edge cases with readied actions and such, so I probably wouldn't (at least, not in a mechanical sense; I'd probably be cool with it as a purely cinematic effect as a GM).