Intersections of the elliptic and the equatorial planes on the celestial sphere are the Vernal Point and the Autumnal Point. Are these two points two antipodes on the celestial sphere of the Earth?
Yes… and no. If the Sun–Earth system was alone in the Universe (or at least in the Solar System), it could indeed be the case. However, the Earth’s orbit around the Sun slowly rotates with respect to the rest of the Universe, so that technically, the points where the Sun seems to cross the celestial equator (a projection of the Earth’s equator on the celestial sphere) are not exactly opposite each other.
However, for all practical purposes, yes, these two points are opposite, being defined by the instant orbit of the Earth around the Sun.