Do shipping discounts automatically apply to a "Pickup To Ship" orders?

Promotions and coupons will apply on Pickup to Ship orders except for quantity based promos. If you have Cart Requirements set up, the discounts won't apply. You will want to perform a manual price override to the shipping cost for this scenario.
The discount will automatically apply if it is a general shipping discount for your club members or customers where Cart Requirements is set to "None".