I have C&C BH here along with C3. (C3/BH)
I can confirm the pairing works well, actually with no switches engaged on BH for me, turning the LF switch on made Havi sound a little off for my tastes. With no switches on the soundstage is wide / mids detailed, I'd actually forgotten how coloured BH sounds after not using one for a while. In my opinion you definitely need an amp if you intend on using Colorfly C3 it simply doesn't have the power to drive these correctly, but sure, sound will come out. Havi even push C&C BH to its test for power, I don't know what others thoughts are but I can max the volume on BH in low gain and not find it uncomfortable.
The power requirements for Havi somewhat remind me of 100ohm ER4S, I don't know what the cable resistance is or where the 32ohm figure came from but I need similar volume on my Studio unit to which I listen ER4S. DX50 has no problem in meduim gain however. High gain with BH there's plenty of juice and I'd be mad to try and max it out. For owners of C3/BH you will be pleased, sounds more expensive than the actual rigs cost combined. For some reason I have a gut feeling Topping NX1 will be a better match and might grab one to loan down the road.