PHEAA has no say over what the consolidation company does. If the consolidation company can provide you with the money to satisfy your debt with PHEAA then you should be able to close that loan.
The PHEAA could be correct that they will not consolidate that debt but if it was already approved I doubt that will happen. These are really questions you need to talk with your debt consolidation counselor about.
PHEAA would love to get the garnishment. Because with a garnishment they will get quite a bit more money as well as the ability to charge fees for their service and basically bloat the value of the debt.
PHEAA will need to go to court to get the garnishment. You have a right to be there. They can not do anything like this fast. To do that they have to prove that you are not attempting to make good on your debt. Which is why it is a really bad idea to ignore student loan debt. The best thing you can do is keep trying and get in writing from them any of their requests, demands, or threats. And also keep track of your communication where you are trying to make good on your debt.