Clamp-on brake for undrilled forks?

Has anyone used one of these clamps for the rear?

I'd be using it to get myself and the bike to the track and don't want to clamp anything to the carbon forks, and I won't do 85" breakless.

I don't know about the brake but I wouldn't ride that gear all the way there - you'll be knackered! I'd get a flip-flop rear wheel if I was you (you could always put a stupidly spinny gear on the other side and fixxie-skid your way down, save on brakes!)