Does Shady Spectacle copy empowered status of a unit?

No, Shady Spectacles does not copy the empowered status.

Copy effects copy only "copyable traits" — a card's printed (or previously copied) traits, including its rules text. Per the official copy effects rule: "Nothing appended or granted will be seen by the copy effect." The empowered status is a granted/appended state applied by activating the Empower keyword, not a printed trait — so it is invisible to the copy effect.

The equipped unit will gain the chosen unit's name, type, Might, rules text, keywords, etc., but it will arrive without any empowered (or disempowered) status, regardless of whether the target was empowered. It would need to be separately empowered after the copy takes effect.

(Rule 472.1.b.3 — Copy effects copy copyable traits; appended/granted traits are excluded.)