Yes, you can use the classic controller. Gamecube setup is similar to Classic controller.
The GB Player one? Unfortunately not...See, it uses only the Control Stick for movement, and the pad registers as the D pad on the GC controller.
Good game, I don't know why people insist on bitching on this port. It's great, and If you can think of a Cheaper way of getting Metal Slug 2, I don't know what....
Also, MS6 is a great edition to the series. Second best in playability to 3.