Surely you can; but the aux output follows some standard for compatibility. Aux output is designed to be fed into a power amplifier.
In this particular case, the speaker is a low power one and connecting the aux output to the speaker may work but you cannot connect that directly into ANY aux input without checking the voltage levels.
Aux signals are what is called at line level; they are usually output from the preamplifier after equalisation, mixer etc and are designed to be fed directly into a power amplifier.