Adding another higher harmonic to each sound makes the missing fundamentals even more noticable. The only difference between whether ones hears synthetically or analytically is how the listener concentrates on the complex sounds. The auditory receptors in the cochlea separate complex sounds into their component frequencies and loudnesses and forward them separately via the auditory system to the brain. The brain constructs the perception of pitch from this information. If the auditory system is subjected to a harmonic series, the brain computes the frequency that would give rise to this series - the missing fundamental.
Further Reading Go here for a demonstration of virtual pitch or the missing fundamental.