Not really, at least not a 100% - DVD drives have a firmware of their own, the BIOS merely interfaces with them. IDE drives are very much the same - they have their own logic board, firmware, cache etc., they merely serve the host device upon request.
Long story short, just because two ports are on the same motherboard does not mean that you can re-direct inputs between them or point one to the other. In this case though I think it can be done, as there are clearly games that utilize USB accessories of all sorts.
EDIT: A quick Google search and a psx-scene browse seems to confirm my suspicions - you'll need an adapter to convert the controller input signal into something the PS2 can understand, meaning you'll have to use the controller port.