It will probably work, but 4k@60Hz will definitely cause you problems. However, I would advise against it.

I'm concerned that my monitor only supports freesync on the dp, which is supposed to come with the next update. :D

Have you already tried this? I'm interested because I'd also like to use it that way... but I don't know if it works that way. It would be from hdmi to dp and not the other way around. Does anyone know? Lg