The meaning of steady state might be a problem. After a very long time, everything might be photons and neutrinos (after black hole evaporation, and after any possible proton decay with the resulting positrons annihilating the existing electrons). I still doubt that the He could ever be over 1% of the H.
I'm assuming that H was distributed (with some density fluctuations) uniformly at the same density as baryonic matter now, and then it interacted, while the expansion factor remained constant. However, in a true steady state model, nothing would change, and the He:H ratio wouldn't change. There is no a priori equlibrium ratio unless there is a high-temp period or perhaps proton decay.