No. Quark software can only be run on the operating system on which it was installed and activated.

According to our End user License aggrement ,end users who have purchased a single-user License may Install and Use the Software on two desktop computers for non-concurrent use only.

For more information, go through the link - EULA

If you want to use your QuarkXPress or QuarkCopyDesk software on both your primary and secondary computer, such as a laptop, simply install the software on two computers on the same platform. This feature is available only to the primary, registered user of QuarkXPress or QuarkCopyDesk single-user software license.