##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 *[polymorphed][1]<sup>1</sup>*, 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 DM's are allowed to adjudicate ambiguities, and there are none here.

<sup>1</sup><sub>Or *[True Polymorphed][2]*. 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.</sub>


  [1]: https://www.dndbeyond.com/spells/polymorph
  [2]: https://www.dndbeyond.com/spells/true-polymorph