Title says it all.
Will a C&C BH power a Mr. Speaker Mad Dog well enough?
(Max) 300 mW per channel into...?
It doesn't say. 300 mW into 16 ohms doesn't mean it can do 300 mW into 50 ohms. 300 mW into 50 ohms doesn't mean it can do 300 mW into 16 ohms. Also, what distortion level? (though, for a portable solid-state amp, usually you'd expect the distortion to be fairly low until the clipping point...)
It also depends on how loud you want to listen. The louder you listen, the more power you need.
I don't know how much variation there is in T50RP drivers and how much consistency there is in the Mad Dogs mod, but Tyll measured 0.52 mW required for 90 dB SPL on the sample he got at InnerFidelity. For a really loud level of 110 dB SPL, that means 52 mW is required.
There are a lot of blanks to be filled, but if all figures are to be trusted, I would say that most likely the amp would have enough power for your listening purposes. No guarantees about sound quality, but that is probably okay.