Yes it does, but honestly it's not powerful enough to take advantage of any serious gaming features anyhow. That's a pretty low end card and is only going to be capable of very low gaming settings on most titles. Still, it does support directx 12, at least to some degree. It's doubtful we'll see any serious implementation of DX12 for quite some time anyhow, so it's not even an issue for the time being.
http://www.gamespot.com/forums/pc-and-av-hardware-909394553/amd-releases-list-of-compatible-directx-12-gpus-ap-32058329/