Your 'A' calculation is the way you need to be heading. The current rating of the pin isn't what it will output, it's how much current can flow before it is damaged. The current flowing depends on the voltage on the output, and the resistance of the load. It has resistance of it's own which will limit the current it is capable of producing, but in most cases it will try to provide more than it can withstand and ultimately fail.
I disagree with the statement that your math is irrelevant because the Arduino is DC. You can pulse DC to create a square wave at a frequency of your choosing. Frequency implies AC. It is true however that when dealing with AC, you need to speak in terms of impedance rather than resistance, since no speaker has flat impedance from DC to kHz and beyond. Therefore the current it uses depends on the frequency of the signal. On the flip side, most devices don't instantaneously die when their current threshold is tripped. Too much current is usually a problem because of heat, which builds up over time, eventually causing damage.
Way more than you wanted to know I'm sure, but to say electronics is easy would be a disservice.