Should do I think - if the converter lets it work in windows, then it will work in mame. (in theory). Do a search for "driving controls" - its a bit more complicated than it first appears.
Arcade driving games use wither a 360 degree wheel (free spinning, does not return to centre - super sprint, pole position, super off road etc..) or a 270 degree whell (doesn't turn full circle, returns to centre - spy hunter, roadblasters, outrun) and apparantly using one with the other does not work well. Your psx wheel will be a 270 (I believe) and should work with those games.
Having said that I don't use psx kit on a pc, so I'm assuming there is a driver that works in windows that is used with the converter box to allow it appear as an input device that windows recognises.