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I honestly doubt but I can neither confirm or deny it. I am on Parallels Desktop 13 and it is working flawlessly.

https://kb.parallels.com/en/124223

It doesn't seem to list Mojave under the compatible operating systems but perhaps that is because it is still in beta.
 
I can confirm that parallels 12 is "working" on Mojave Beta 7. I only booted to the desktop of my Windows 10 machine and opened a few apps. Not sure if it is 100% stable or is there are any issues that come up under specific circumstances.
 
You should have received an email from Parallels these days whether your version will work with Mojave final.

I assume that Parallels 12 will stop working with Mojave, as, similar to Parallels 11, even High Sierra is listed as not fully compatible with Parallels 11 and 12 already.

https://kb.parallels.com/114381

Also from experience with many older Parallels versions i had and that worked during the beta phases, once the GM / final was out, stopped launching, forcing me to upgrade.
 
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