can i use a usb to parallel port adapter to connect breakout board to computer? (using mach 3)

Unfortunately no. The parallel port allows for digital signals to be output from 17 pins simultaneously (in parallel). Parallel port adapters tries to achieve this by receiving instructions in a two wire (USB) data signal and convert that to 17 disparate signals. This type of data transmission is too slow for the drivers of a CNC machine or router.