Do you mean offroad tracks (roads that aren't paved and are displayed on the minimap) or pure offroad (mountains and deep inside forests)?
If it's the former, as far as I know, yea, they do go at high speeds (tested a Street Race-spec Skyline, the C3 Racing, and the X-Class Rally Raid).
If it's the latter, I believe only rally raid cars can go at high speeds - anything else will struggle (even Rallycross cars)