I haven’t used any of what you describe, but if its like other distros you shouldn’t have an issue. It would be best to have the installer put the bootloader on the external drive so you can move it to a different computer if you want (and to prevent it messing with the PureOS bootloader, though I don’t know if it would or not).
I think Pureboot will boot off of USB. Grub should be able to see it if its plugged in, so you can update-grub from PureOS and have it in the grub list (and then probably have it default to boot PureOS after 5 seconds or something so you don’t accidentally try to boot Qubes when it isn’t plugged in).
I’d say your main concern is the Qubes installer, but you can see if it’ll offer the option to install to the external SSD without committing.