according to the
pinout the bottom 12 pins are for the 12 inputs in a 12*1 "matrix" with inherant NKRO. The tops are gnd, reset, LED's, pair, and UART. The side appears to be FTDI, but in reality is not usable after adafruit programs it (they use those pins to program it at the factory)
So with custom firmware, you can get up to 6*6=36 keys, or maybe more, depending on if you can actually use the top pins as inputs.
more information might be had from the datasheet of "The module consists of a CSR BlueCore" that they "custom program".
Doesn't the teensy have UART? you could just use it to output keys via that (9600 buad, 3V or 5V) and have bluetooth OR USB. You are limited by what codes it'll take, but there's a good number (looks like most keys are there)
http://learn.adafruit.com/introducing-bluefruit-ez-key-diy-bluetooth-hid-keyboard/sending-keys-via-serial