And you have to spend 8 kg of O2 per 1 kg of H2, raising the molecular mass from 1 or 2 up to 18, thus: dramatically decreasing the ISP and increasing by an order of magnitude the spent mass, in the rocket equation.
So, it eats the ISP of pure hydrogen. So in the best case it can replace high ISP with high thrust for the same engine, but you don't need it for NERVAs.
If the engine is really hot and the exhaust speed is tens km/s, it's just a bombardment of an oxygen target with hydrogen ions, The oxygen will be just ionized, and turn into a hot cloud inside the nozzle, pressing it from inside.