I know that the Fury X works just fine with a normal BIOS, so I don't see how the 390 wouldn't. I'm pretty sure that if any graphics card is released that supports only UEFI, that fact will be newsworthy.
I don't really see how that would be any benefit to the card maker, though, so I find it unlikely, at least for the foreseeable future.
Now I am relax about it. and I am going to get one R9 390 in 2 weeks and I will Update.
also I found a video that he/she was running MSI R9 380 with Intel duo core 2, so that shows it is working,
his/her user name is "Sssaga Benches"
UEFI is actually really just graphics output protocol which is an extension of the VESA VGA firmware on all video cards. My GTX 660 Ti can work with UEFI or BIOS depending on which setup I am using.
In short UEFI is backwards compatible