No, Server 2012 does not provide software RAID 6 as part of the OS. Your choices with Windows software RAID are still your basic mirroring, striping, or RAID 5 parity.
Storage Spaces in Server 2012 is basically just adding the flexibility to pool different types of cheap storage together, like external USB drives, SATA drives, network storage, etc.
You would need a hardware RAID card capable of doing RAID 6.