Do Shady Spectacles copy on play effects?

No — the "on play" effect will not trigger, even though its text is copied.

Shady Spectacles does copy the chosen unit's printed rules text, so the equipped unit will "have" the "When you play me" ability (Rule 477.1.b.1.a). But a Play Effect only triggers when the permanent with that ability is played to the board (Rule 383.4.a.2). The copy effect applies after the equipped unit already entered play, so its "played" event is long past — the condition can never be met. Same reasoning as the Reflection token ruling (FAQ #11575). Other triggered abilities on the copied text (Deathknell, attack triggers, etc.) work normally after the copy.