If units enter ready, does Pirates Haven activate?

No, Pirate's Haven does not activate if a unit enters ready.

According to RiftJudge FAQ #6918 and FAQ #9115, Pirate's Haven only triggers when a unit is readied, which is defined as the specific game action of transitioning a unit from an exhausted state to a ready state (Rule 415).

Units that enter play already ready, or units that transition to ready via the Accelerate keyword, do not trigger the effect because they are not undergoing the action of "readying" from an exhausted state.