I don’t think they do.
However, you might be able to get a good Pure OS template by using a similar method to the one described in this page (and replacing Kali repos/signature with Pure OS’s). Or you can just install Pure OS directly into a HVM and you will also get access to a Pure OS desktop.
Personally, I would rather just use Debian templates included by default in Qubes and wouldn’t bother with Pure OS.
If you still want to have Pure OS in Qubes and the previous method did not work, I would recommend taking a look at how Pure OS differs from debian and try to modify a debian template from there.
Most of the differences are either installed applications and configuration differences (shouldn’t be too hard to configure yourself), security hardenings (which are mostly redundant if you are already running a VM inside qubes) or desktop environment, which you probably won’t use inside Qubes.
This is a common theme with Qubes. You will need to configure a lot yourself. The appeal with Pure OS is having a good sensible default configuration out of the box where you can just get straight to work.