patrol. How can they know that you are a AOS applicant. However if you show them the receipt of your I-485, you should be OK with border patrol. Likewisely you can not use an expired EAD to renew your DL or to border patrol.
As for DL, some states require 11 months on I-94 or EAD for renewing purpose, so you need such I-94 or EAD to satisfy them.