##Yes, and no. The simulacrum's statistics are replaced. This means you take whatever form of record sheet you're using for the simulacrum, put it aside, and grab the stat block of the creature you've polymorphed it into and use that while the polymorph effect persists.
The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast. It retains its alignment and personality.
While polymorphed1, the creature is a tyrannosaur, a giant ape, or what have you. If that creature has regeneration, it can regenerate because it is that creature. For the duration of the polymorph effect, the simulacrum effectively does not exist, so none of it's restrictions apply to the new replacement.
The target assumes the hit points of its new form. When it reverts to its normal form, the creature returns to the number of hit points it had before it transformed.
When the polymorph effect expires and the creature resumes being a simulacrum, it has however many hit points it had before the polymorph. Of course, that's how it works for any other creature, too.
##Note Adventure's League is not a factor here. DDAL DMs are allowed to adjudicate ambiguities, and there are none here.
1Or True Polymorphed. For the purposes of this conversation, the only difference is the range of creatures you can pick for the transformation. You'll probably need TP over regular P to find something with Regeneration. I can't think of any beasts that have it, off the top of my head.
