Saturn Ion Shutting off

2006 Saturn Ion2, 2.2L, The car seems to run fine with no a/c, strong acceleration, 900RPM idle. When the a/c is turned on at idle, the revs drop to 400RPM and the engine shudders. At speed with the a/c on, the car shuts itself off and throws code U0100(lost communication with engine control module), emissions light, and flashes “PWR STR” and “COOLANT” on the dash.

My theory is: the a/c over stresses the motor, dropping the engine revs, causing the voltage to drop below 10v. The ECU then panics and shuts off the motor. Is this possible? I would like some reassurance before I start swapping out parts in the driveway.

I forgot to mention that when I removed the oil cap while the engine was warm, smoke was coming out. Not a lot of smoke, but it was noticeable.