"Does space require dark energy in order to exist?"

Yes, as long as we continue to assume that cosmological redshift comes from real recessional velocities between galaxies, rather than the accumulation of tiny effects caused by the divergence of the concept of Euclidian distance from the real geodesics that photons trace through spacetime as they avoid colliding with matter particles in the intergalactic medium.

The cosmological redshift effects that we usually attribute to the inherent energy density of space or Dark Energy pushing matter apart would result from the conceptual error of assuming that spacetime is perfectly flat even with particles.