Mac Pro's may not have Quick Sync in their Xeon processors, however they are more than capable of handling it based on their CPU power alone.
I've been using "AirParrot", a third party app that does AirPlay/Mirroring and more. I have a 12-Core 5,1 Mac Pro with an ATI 5770, using iStat to monitor CPU load, AirParrot does a fantastic job. Interestingly, using OS X's native AirPlay on my current gen 27" iMac taxes the CPU more than AirParrot on my Mac Pro.
Give AirParrot a run. Hope this helps.