3.7 V to 12 V boost converter - effect on cell
You won't get as many mAh from the 12V supply as you do from the battery, but you'll get almost as many mWh.
A boost supply can't provide free energy, so when it generates a higher voltage than at the input, it must draw more current from the input than it puts out.  In the ideal case, Po=Pi, meaning Vo * Io = Vi * Ii.  In real life, the power supply will have an efficiency lower than 100%, so Vo * Io = Vi * Ii * Eff.