I just set up a test of this locally, and it seems to work fine, provided that the PDF-X driver is installed on the RDP server and visible to the user.
I ran the PDFX5 installer while logged in on the server console, creating a printer named PDF-XChange Printer 2012. Then I connected via RDP from two different client machines using different logins. From each I then used ATE to connect to a Linux server where I printed a test file using a printer init file that looks like this:
DEVICE=AUXLOC:PDF-X
PASSTHROUGH=OFF
Both successfully created a PDF file on the RDP server. I was also able to save the PDF file on my local PC (since I had added my local C drive as a resource to the RDP connection.) The only problem I ran into was that Acrobat from within RDP session refused to open the PDF file from my local C drive, complaining about some kind of privilege issue.
What I'm pretty sure you will not be able to do is use an instance of the PDF-X driver installed on the client. Since PDF-X is licensed per workstation, it's not surprising that it doesn't allow access to instances shared across a network. It's surprising enough that it works within RDP, since that would also allow many users to share one copy. (Note that this isn't an issue for the A-Shell license for PDF-X, but it would be if you were buying the retail license which is sold on a one-user one-pc basis.)
I didn't try it with PDFX3, but I can't see why you would want to use the old version in this case.
If you're still having troubles, the intermediate test I would suggest is to just bring up Notepad within your RDP session and see if you can print a file to the PDF-X driver there. You'll get the not-licensed stamps, but that will at least verify that you can access the driver from the RDP session. And if so, there's no reason why ATE couldn't also do the same.