Unfortunately...no. I've checked in to this before for myself recently. Limited release pins are "blocked out" of mail-ordering for the 1st 30 days of their release. After that then they can be ordered/purchased without having to go to the parks if there are any available.
Open release pins can be ordered beginning day one of their release. I usually get the SKU from the Disney Pin website and call Disney Parks Merchandise: 1-877-560-6477 (M-F 9:00am - 8:00pm Eastern Time).