Is it possible to program the Teensy3.0/3.1/3.2 in C?
Basically the teensy board is a Cortex M4 from Freescale (MK20 family). So you can download the Freescale toolchain and create a project totally in C for the MCU inside the Teensy.

But you need to create a JTAG connection between a debugger and the MCU if you want to debug/program it.