Yes, you do.
Regardless of whether a lens is designed for DX or FX, on a D300 you would still multiply by 1.5 to get the 35mm equivalent field of view.
200mm DX == On a DX body, the same field of view as a 300mm on a 35mm body.
200mm FX == On a DX body, the same field of view as a 300mm on a 35mm body.