I don't think I understand the question.
Are you running a neutral with the 208V?
Or are you running 208V, 2 wires, and you want to use the 120V input to a ballast to get 120 volts out??? I guess if the ballast input was an autotransformer, it might just work, but I don't think it would comply with the code. The ballast wouldn't be listed or rated for running another fixture.
Steve