Can a PEARL open a two position outside damper?

Yes.

The PEARL can either us the (G) or (E) output to open a two position outside damper.

Note: The two position damper must have a 24 Vac power-open/spring-closed type actuator.

Open the outside damper anytime the supply fan is running:

You will want to use the Pelican (G) output to enable both the supply fan and open the outside damper.

Open the outside damper only when an economizer cycle is active:

The default sequence for the PEARL’s (E) output is to energizes when the an economizer cycle is active. You will want to wire the (E) output to open the outside damper.

Open the outside damper only when Demand Ventilation cycle is active?

The default sequence for the PEARL’s (E) output is to energizes when the a Demand Ventilation cycle is active. You will want to wire the (E) output to the outside damper.