If you can get a loan with USAA right now I would do it. Depending on your credit they have super low rates (I saw them offering .99% recently I thought) with good credit and the discounts they are offering. You can also get some deep discounts in shopping through the Autofinder service they give, and that gets you a small reduction on your interest rate on top of what they offer you.

How did you get an account? You have to be linked to somebody in your family that served in the military. If it is your spouse by chance, you should just have them take out the loan in their name because you will save a lot I think if you go that route.

I don't know if telling them you have an EAD card would work, but I think it is logical to assume that it would and the worst that could happen is that they could ask you to close the account. You could also try calling them to ask about it without giving them your USAA number.

If you do get a solid answer, please do share what you found out because I am curious to know.