The group scheme G_a here is the one-dimensional additive group.
Principal Ga-bundles on a scheme X, in any of the Zariski, etale, or flat topologies, are classified by the coherent cohomology group H^1(X,OX). For a smooth complex projective variety, this is the antiholomorphic component of the de Rham group H^1(X,C), which is a topological invariant. So (in this smooth Kahler setting) the existence of nontrivial Ga-bundles depends only on the topological type of X.
I omitted some underscores for typesetting reasons.