The gear does not provide that much drag in reality
I do not agree. I cannot speak for the Chinook. But, wheels down in the water with any forward speed is real trouble in a flying boat with wings, and flying boats with wings (and a tail) have much more authoritative pitch (nose up) control than a conventional helicopter.
I cannot see how the helicopter could manage any better that the flying boat. If you tried a wheels down takeoff in a flying boat or float plane it would go over, though probably with some warning to the pilot. He would have pitch control to use to resist the nose over, while he reduced the power.
With all the drag on the bottom, all the thrust at the top, and no ability to control forces in the whole aircraft pitch axis, it seems pitching over is inevitible for the helicopter, if you tried a running takeoff on water with the wheels down (those long looking dual nose wheels can't help either). Perhaps the Chinook can manage better because it is tandem rotor, and I presume has much greater pitch control.
I recall a spectacular photo of a Vertol 107 towing a load on the surface, it had an incredible nose low pitch attitude, and I presume was in stable flight. That photo makes me think that with a high "drag" force on the lower portion of the helicopter, it would like to assume a very nose low attitude to fine stable flight. This helicopter just found the water with the blades before it got to the stabilized nose low attitude. The forward sponsons of the Sea King having the bouyant effect forward of the C of G, is an interesting observation in light of the other considerations.
Pilot DAR