Mott-insulator-to-superfluid quenches have been used by recent experiments to generate exotic superfluid phases. While the final Hamiltonian following the sudden quench is that of a superfluid, it is not a priori clear whether the final state of the system actually enters the superfluid phase. To understand the nature of the final state the temporal evolution of the momentum distribution is calculated following a Mott-insulator-to-superfluid quench. Using the numerical infinite time-evolving block decimation approach and the analytical rotor model approximation it is established that the one- and two-dimensional Mott insulators following the quench equilibrate to thermal states with spatially short-ranged coherence peaks in the final momentum distribution and therefore are not superfluids. However, in three dimensions a divergence in the momentum distribution indicating the emergence of true superfluid order is found.