Well, to be more precise, you need DisplayPort because FreeSync is basically an AMDs implementation of VESA DisplayPort Adaptive-Sync.
In case of FreeSync over HDMI, it's AMDs implementation of VESA HDMI VRR draft specs. Now HDMI VRR specification has been implemented in HDMI 2.1 standard.
So, physical connection is irrelevant because DVI doesn't supports required protocols. Adapter won't help