Presumably, the intergalactic medium (IGM) should get less dense as the universe expands. Also presumably, There should be a Hubble redshift to absorption lines due to the IGM. Could this provide an independent measure of cosmic expansion vs time?
Partially random motion of galaxies due to their gravitational interactions would stir up the IGM a bit and smear the data, but maybe not so much as to make the data useless. The "local" smearing ("local on the scale of large galaxy clusters) should be more or less isotropic, so perhaps even with this type of smearing a strong IGM velocity signal could be extraxted from spectral absorption data.
Has this kind of study been done? Is it currently being done? Is it technically feasible?