If I were to build a circuit that took voice and converted it to PFM (pulse frequency modulation) and feed that into the input of a radio would someone be able to hear my voice?
Not directly, if the radio is modulated by a PFM subcarrier, which is what you seem to be describing.
Would the radio even work with a PFM imputed audio stream?
What radio? Pulse Frequency Modulation is similar to FM, except that the carrier is a train of pulses instead of a sine wave. You vary the frequency of the pulse train to modulate it, just like you vary the frequency of a sine wave carrier.
If you directly PFM a transmitter, then I believe a standard FM detector would recover intelligible audio, but a lot depends on the unknown details.
If you PFM a subcarrier and apply that to to a standard transmitter, which is what I think you're trying to describe, the demodulated output of the receiver should be a copy of the PFM signal modulating the transmitter at the other end, which would require another level of demodulation. That's a variation of what's happening in multiplexed signals, like FM stereo.
What's not being taken into account here are things like occupied bandwidth, and the feasibility of frequency modulating a pulse train, and being able to apply it to a voice grade transmitter, and not exceed the audio or channel bandwidths of either the transmitter or receiver. I don't think it would be possible without fairly wideband RF hardware. The pulse frequency has to be high enough to contain the highest voice frequency and it's sidebands, so will be inherently wider than just the voice frequency alone. I don't know what the sidebands of a PFM signal would look like, but I expect it to be similar to FM sidebands, except worse.
The rise and fall times of the pulses will add to the occupied bandwidth. Squeeze it into enough filters, and it starts to resemble a sine wave... a frequency modulated sine wave. And that's easy to demodulate.
Sounds like a lot of effort for...?