Yes, Intel Xeon E3 1226 v3 supports Quicksync video. To know the exact configuration and support for your specific motherboard. Please refer to ark.intel.com . where you can select and filter all the Xeon family hardware supporting Quicksync.
That motherboard along with that CPU should provide quick sync capabilities, but it is important to know that the various packages supporting Intel Media SDK do not always offer support for the low end CPUs, in particular in some cases only support is offered with the highest numbered CPU.
I am not an Intel representative.
This document: https://software.intel.com/sites/default/files/managed/12/a9/media_server_studio_getting_started_guide_linux.pdf tells that only 128x CPU are supported.
If it is so than it makes QuickSync not interesting for commercial purposes.
Please, can you officially confirm or not confirm that 1226 is supported with the latest quicksync SDK?