Yeah generally peak efficiency is around 50% to 60% of PSU rating.
That being said for high end 80-Plus Gold PSU the curve tends to be very flat. So while 80% loaded may be less efficient it may only be 3% or so less.
Some PSU provide the efficiency curve. The bad news is most don't.
According to this, a 1500w Gold-rated PSU would supply the same DC current to my rig as a 1200W PSU, but would draw less Wattage AC at the wall?
Yes a larger PSU isn't going to use more power it likely will use less power because it is operating at a higher efficiency for a given load.
Important should this rig find a place on my only free power source, consisting of one 20amp circuit.
A dedicated circuit is always best but you can use other circuits depending on what is on it.
A 120V, 15A circuit shouldn't be loaded more than 80% for continual loads. That is ~1400W. If you have 1100W DC @ 88% inefficiency you are looking at 1250W AC. That is going to use up most of a 15A circuit.
Lastly, an AX1200 would definitely suffice for this set up?
AX1200 should be fine if it is a DEDICATED mining rig going w/ the concepts above (sempron, usb linux, underclocked memory, etc). A larger or dual PSU would increase efficiency slightly.