Even the latest HP ALM-Synchronizer, 12.20 does not ''officially support Windows Server 2012.
(see: https://hpln.hp.com/page/hp-synchronizer-alm-and-qc-technical-specifications)

It *might* work (I expect it would work just fine), but if there is some ''quirk'' in it's base behavior (having nothing to do with the adapters or links you are using), HP may not support you since the OS is not ''officially supported''.

Synchronizer does not usually get ''patches'', so I would keep a lookout for a new VERSION (new version number different than 12.20) of Synchronizer that may support it.
Now, HP generally releases versions of HP-Synchronizer along with major releases of QC/ALM, and since QC/ALM12.20 just came out a few months ago, it may be some time before they have a new major release.