First your graphics card must have a HW mpeg converter in it. I think about all ATI have them now and probably a lot of the newer high end Nvidia card. You will have to check the specific model.
Next the conversion type you are doing has to match the HW in the video card. MPEG 4 at certain resolutions should be supported, probably not find AVI converison support, etc.
Finally the drivers that the video editing program uses must support HW acceleration of your particular card.
That means researching your specific HW, SW and plans. I'd look on a video editing specific forum. The card vendor sites tell you next to noting about capabilities.