Upon increasing the strength of Rashba spin-orbit coupling., induced by a synthetic non-Abelian gauge field, a system of fermions at a finite density rho approximate to k(F)(3) evolves to a BEC-like state [J. P. Vyasanakere, S. Zhang, and V. B. Shenoy, Phys. Rev. B 84, 014512 (2011)], even in the presence of a weak attractive interaction described by a scattering length a(s). The BEC obtained at large spin-orbit coupling (lambda » k(F)) is a condensate of novel bosonic bound pairs of fermions (called ``rashbons″) whose properties are determined solely by the gauge field. Here we investigate the collective excitations of such superfluids by constructing a Gaussian theory using functional integral methods. We show that there is an emergent Galilean invariance at large lambda, and the phase stiffness is determined by the rashbon density and mass, consistent with Leggett’s theorem. We further demonstrate that the rashbon BEC (RBEC) is a superfluid of anisotropic rashbons interacting via a contact interaction characterized by a rashbon-rashbon scattering length a(R). We show that aR goes as lambda(-1) and is essentially independent of the interaction between the fermions as long as it is nonzero. Analytical results are reported for high- symmetry gauge fields.