Is it bad that my cordless drill is smoking?
Don't Stall Electric Motors. Ever.

Stalled motor = no back EMF = High Current.

It burns the windings out.

I'd think the technology in more expensive drills with brushless motors would sense a stall condition and go into shutdown, but yours seems to be willing to sacrifice its life, cooking the insulation off the windings and attempting to burn out the MOSFET array that drives the motor.

An Electric Impact wrench is more appropriate for this kind of abuse. It has a mechanism that allows the motor to spin up, deliver a sharp shock to turn the bolt and release immedately so the motor never stalls. 

If an electric or pneumatic impact wrench driving the appropriate impact socket won't loosen it, the time has come to apply some Mouse Milk and a breaker bar.

Here's a Dewalt Planetary Set with attached Brushless Motor. Your windings will be dark brown instead of that gold, green or red color they usually color the enamel. The next step for it is to turn black and the windings then start to short.