PDFX doesn't contain a viewer, although the people who make the PDFX driver also make a viewer that can be licensed in such a way as to allow you to distribute it yourself or bundled with ATE (which might be an advantage over relying on the presence of Acrobat Reader, which you are probably not in a good position to distribute). It would even be possible to license and configure their viewer such that it appeared to be built-in to ATE (and maybe even launched in a window you controlled). But that would require some financial commitment.
On the other hand, given the prevalence of PDFs these days, it wouldn't be unreasonable to simply require that any of your end-users who want this feature to acquire and install whatever PDF viewer they want.
Furthermore you would almost certainly need to make the PDF file visible to the Windows client by some means. I would suggest just file-transferring it to the client workstation prior to launching the viewer (via MX_SHELLEX so you don't need to know the details of the viewer).
A slight variation of the approach would be to specify a file-based URL, thus putting the user in the same position she would be in when trying to view a PDF on the web (i.e. either use a PDF-reader plugged-in to the browser, or re save it somewhere and launch it manually, etc.)