Is the vernal equinox always in zenith somewhere on the equator?
The Vernal Equinox is defined by the point where the sun's path across the sky, the Ecliptic, crosses the Celestial Equator. It is always going to be on the Celestial Equator.

Given the various ways that objects in orbit over Earth are perturbed, any set of keplerian orbital parameters that describe the orbit of any object over the Earth (including the Moon!) will need updating long before the drift of the Vernal Equinox along the celestial equator becomes significant.