Can installing Xen drivers to PopOS let me use Qubes to send files in and out?

You mean like with Windows qube with Qubes Windows Tools installed?
For this you need to install Qubes tools in the PopOS but they are not available for it.
Since PopOS is based on Ubuntu then maybe you can install the Qubes tools packages for Ubuntu that @unman provides:
https://qubes.3isec.org/