I am looking for pointers/tips on how to generate a synthesized sound signal on the BeagleBone akin to watch the tone() function would return on a Arduinos. Ultimately, I'd like to connect a piezo or a speaker on a GPIO pin and hear a sound wave out of it. Any pointers?
The GPIO pins of the AM3359 are low-voltage and with insufficient driver strength to directly drive any kind of transducer.  You would need to build a small circuit with a op-amp, transistor or FET to do this.
Once you've done this, you'd simply set up a timer loop to change the state of the GPIO line at the required frequency. 
By far the quickest and easiest way of getting audio from this board is with a USB Audio interface.
How to generate sound signal through a GPIO pin on BeagleBone