Are you referring to this post Many rotated_lorentz(1) constrains - Very slow ?
I will defer to someone else on possible use of geo_mean , but I can tell you that CVX converts 2 by 2 LMIs (and some other LMIs for which it figures out how) into SOC constraints before sending the problem to the solver. So I suppose that if you enter them as SOC constraints rather than LMIs, you may save whatever time it takes CVX to do the conversion - I don;t know whether that is a significant time or negligible.
I think what mcg is getting at in the link is that you will save a lot of CVX modeling time if you can enter a vectorized formulation which avoids for loops to the maximum extent possible, whether that involves use of geo_mean or otherwise. One or tow big rotated cones or geo_mean cones are better than larger numbers of “little” ones in terms of CVX modeling time.