Playing sounds with only one frequency at a time
Yes, as long as we are also allowed to vary the amplitude versus time and we're allowed any time period in which to change frequency. Any single valued waveform can also be described in terms of instantaneous frequency versus time, where the instantaneous frequency is the derivative of phase so in this case the rate of change in phase at any given point in time.
If the OP is referring to FM modulation itself (encoding the instantaneous amplitude of a real waveform to the frequency of a constant envelope sinusoid), then yes this is also done where the parameter that can be varied is the frequency deviation (linear mapping of waveform amplitude to frequency) resulting in the modulation index and ultimately the bandwidth required of the modulated signal.  This modulated signal would need to be demodulated with a frequency discriminator to recover the original waveform.