I have not tried this myself but based on similar queries and answers regarding trying to use a Oculus Rift on a Mac while for example the FirePro D700 has sufficient power to support the Oculus Rift it is not recognised and accepted by Oculus even when running Windows via Boot Camp.
The Apple cards in the Mac Pro 2013 are not standard cards and therefore get rejected by the Oculus driver.
I would therefore not be surprised with a similar situation regarding the HTC Vive.
Note: Steam have a VR performance test tool however I suspect it only checks to see if your computer has enough performance and does not prove the software will accept your configuration. See - http://store.steampowered.com/app/323910/
There are rumours that next year Oculus may start supporting Macs and OS X officially but I would also expect this at least in some cases may also be in anticipation of new Mac models.
So, if you run the above Steam tool via Boot Camp and Windows it will at least show you if your Mac is fast enough.
Ironically, if you had an older classic Mac you could fit a genuine Nvidia GTX-970 which is approved for HTC Vive. You would still need to use Windows and Boot Camp.