It should. And this is the problem, with the number of TV setups out there it may still give you trouble, but it's not the interface that's the issue.
I have seen people complain about 1080P and 1080i TVs not working on every card since the R9xxx GFFX series. There's no reason why it shouldn't work, but as I mentioned before you may have the niggling issues everyone gets like overscan etc.
Funny thing is my HD2600 works like a charm 99.44% of the time, and then I plug it in at one location (work, GF's, etc.) and then return home and plug it into the 1080i TV and voila, can't get it to work right away, trouble detecting, etc. Reboot, doesn't work. Then change resolution, still doesn't work, then reboot, and voila, back to normal.
PC to TV is just annoying mainly because they don't follow the same standards and there are so many variables. But that being said, sometimes on my TV my HDMI connection or component connection won't properly recognize the HD/BluRay player or even the progressive DVD player and I get a Blue screen or weak signal until I turn on/off the TV, and those are supposed to be dumb industry standard parts. So it's not just PCs / Graphics Cards.
Anywhoo, it should have no trouble supporting that resolution through a DVI->HDMI dongle, but you may need to tinker and tweak to get it to work the way you want with your TV. Based on most people's feedback you may find yourself tweaking the advanced TV settings once you get it setup.