Please remember that this report is purely anecdotal.
I delayed upgrading my iMac 5K from El Capitan to Sierra until macOS 10.12.1 was available -- i.e., I never tired to run Parallels Desktop 11 under Sierra 10.12. As soon as I'd finished the Sierra (again, 10.12.1) upgrade, I encountered instability and system freezing when Parallels was running. This crashing ranged from locking up the whole iMac blocking input from keyboard and mouse, something that I've almost never seen in my 2 years with this computer, to coming out of sleep mode showing nothing but a black screen on both the iMac display and a secondary 4K display with a movable arrow cursor that was rapidly replaced with a movable perpetual beachball, something I'd never seen before.
Since this is a production machine, I didn't have the time to troubleshoot it further. I hadn't planned on upgrading Desktop 11 because of reports, like those in this thread, that it would work with Sierra, however, I don't mind too much spending $50/year to keep it current because it's critical on my setup. I therefore, did the Desktop 12 upgrade, and the instability vanished immediately. Cause and effect???
Did an incompatibility between Parallels Desktop 11 (latest build) and macOS Sierra 10.12.1 cause my three hard crashes? I cannot be positive, as I didn't have time to troubleshoot it. Likewise, did the Parallels Desktop 12 upgrade lead to resolution of the crashes? I cannot be sure. Both could have been coincidental. It's not unheard of in the computer world for an upgrade to require more than one reboot to be stable, however, I was still having problems after 3 or 4 reboots.
Conclusion: I'm suspicious that macOS Sierra 10.12.1 and Desktop 11 could have a serious incompatibility. Again, one is unwise to draw firm conclusions from an anecdotal report, but at the same time, I think it's the better part of valor to report what I experienced in case it happens to other users.