In experimental proposals published in the last two decades, a so called frozen spin storage ring concept was proposed for setting upper experimental bounds to electric dipole moment (EDM) of elementary particles. In a recent paper of ours, a fully covariant general relativistic (GR) calculation was presented on the Earth's gravitational modification effect in such mixed magnetic-electric frozen spin storage ring on the spin transport, which could contribute to such measurement. It was shown that similarly to an EDM signal, GR causes a spin precession out of the orbital plane, under the frozen spin condition. The rate of the vertical polarization buildup is predicted to be -a*beta*gamma*g/c, where g is the gravitational acceleration on the surface of the Earth, c is the speed of light, beta*gamma is the particle momentum over mass, and 'a' is its magnetic moment anomaly. It is seen that the effect increases unboundedly with the Lorentz factor gamma. Moreover, it is proportional to the magnetic moment anomaly 'a'. This paper mainly addresses the experimental perspectives to detect this effect in a realistic frozen spin storage ring configuration. Such a measurement would provide a novel test of GR, sampling the tensorial nature of GR at a microscopic level, as acting on the spin vector of elementary particles. The conclusion is that the pertinent GR experiment seems to be realistic with large magnetic moment anomaly particles, such as tritons, helion3 or protons, whereas it is not realistic with small magnetic moment anomaly particles, such as deuterons, muons or electrons.