i think, it should work... i have a 34uc88 lg display, it supports the freesync from 55-75hz, and officaly just via the dp.
i did some indirect tests, first with a 9800pro. i used my dell 2007fp monitor to test the resolutions:
* the dvi output converts the lower res to 1280x1024 75hz
* the vga output is direct, it showed me 720x400 70hz correctly
i tried with a simple dvi-hdmi adapter to connect to my lg display, unfortunately this monitor does not show any information about the input:
* the dvi output (it must be 75hz! 1280x1024) showed well
* i cannot reach higher res than the 1280x1024, no image (on the dell worked well with 1600x1200 eg)
* i could change the frequency, it worked, but i am skeptical, it really set the selected values, because the 200hz also accepted, and showed image
second round with a 8800gtx (on the dell first):
* the dvi output detects somehow the input capabilities, it sets always 1600x1200 60hz (this is the maximum for the dell) - it uses this constant values always
* on the lg... i could set 16:9 resolutions up to 1920x1080 but with fixed 60hz
so, if the vga-hdmi converter outputs the original resolution and frequency, there is the chance, my monitor can handle it. it would be the best case, because, if there is an internal conversion, it depends on the vga-hdmi converter (and we need a scaler).