This question is explicitly answered in the FAQ. From page 13 of the printer-friendly version:
FAQ version 1.8 wrote:
Q: If an enemy is put into play directly engaged with me, has that enemy “engaged” me for the purposes [of] Forced effects or Responses that trigger from engaging an enemy?
A: Yes. An enemy that enters play directly engaged with a player has engaged that player.
The word "of" is missing from the FAQ entry, but that's a typo. The answer is yes, the "when Cunning Pirate engages you" text will trigger.