Controller support in Cardboard is entirely up to the specific app. Since the GearVR controller isn’t normally used outside of GearVR, I’d guess it won’t work at all, but it’s possible one or two of the buttons might be mapped to something. The touchpad and gyro very likely would never do anything.

I have a cheap Bluetooth Red Samurai pretty close to this and it works fine. Feels cheap, but for the price I am very happy. Has a keyboard and controller mode, which is nice for compatibility.