The headphone jack sends out an analog signal from the DAC. Even if you tried to fake a digital bitstream (I doubt you could manage the voltages necessary for normal logic levels anyway) the bandwidth would be much too small to transmit audio this way. Even if you assume that a pure sinusoid could act as a digital signal the bitrate would be capped by the maximum frequency produced by the DAC (usually close to 20 kHz). So, you could maybe get 20 kbps even under the most naive assumptions. I'm sure other objections exist as well.