In my old car (91 2.0SI), I was running a Fosgate 400A4 - at 4 ohms pushes 50*4 (rated, actually higher for Fosgate). This worked with no problem.
I then put in a sub and bridged the two rear channels to it, which upped the draw a little more, still with no problems.
The final stage, I ran the 400a4 as originally set, put in a Fosgate 250a2 bridged into the 12" sub. The "birth certificate" for the 250 had it rated at well over 400W. That's when things started getting funky, then again, I was pushing well over[b/] 600W. Lights would dim when the bass hit and I ran the battery down with the car running if I played it really loud for extended periods (over 45 min).
The bottom line is that if you're only running a 50*4 amp, don't sweat it.
As far as amps being the main concern, sure that's totally true. But putting more and/or higher powered amplifiers will draw more amperes (amps) from the system. It's been a while since physics, but I believe the relationship is:
Volts * Amps = Watts
Since most accessories, including stereos and amps are in the same volt range (12 -14V), if you have a higher Wattage, you're going to be drawing more amps off the system.
As far as the AC question, the AC shouldn't matter too much since it's mechanically driven.