I understand that an RCD is a device that interrupts an ac circuit (usually in outlets) if current between live and neutral/ground is not the same, indicating something is wrong with the circuit. It is in a closed state (the power is connected to the circuit) when two wire coils (live and neutral) on the same core oppose each other (as they normally do), cancelling out their magnetic fields. However when these coils do not oppose each other or vary enough to produce a net magnetic field they trigger a sensor which opens relays that disconnect the circuit. In practice this could be done when someone touches the live wire for instance and are connected to ground (which is connected to neutral on most modern systems). But my question is in an ac circuit wouldn't shorting out or allowing current flow between the two wires not vary their relative currents because they are already connected in the ac generator and the electrons that pass through the person (or connection point) would just join the alternating flow that already exists (at higher currents but still at the normal 60hz oscillation/opposition between live/neutral)?
As Martin hinted in his comment, an RCD is most usefull in a situation where a fault is likely to cause a current flow to ground/earth. This is actually a very probable situation for a fault: touching one wire (while being somewhat ground-connected) is much more likely than touching two wires simultaneously. And it doesn't need to be you: the compromised live wire could touch a grounded part of the appliance.
In my country (230V, both wires live) there are generally two classes of appliances: metal casing earthed, and insluated casing 'double isolated'. In this situation a RCD is very usefull for detecting a compromised wire touching a metal part of an earthed appliance.
Primary purpose is to prevent a short circuit from causing a fire. Fuse, however, is too slow to reliably protect a person from electric shock.
RCD (aka GFCI)
Primary purpose is to protect from electric shock. It's a lot more likely that a human touches only the hot, rather than hot and neutral simultaneously.
In an artificial [contrived] scenario, it is possible for an RCD not to "notice" a short. There should be, however, a fuse somewhere upstream of the RCD which will open as a result of a short.
(source: EDN article)
By the way, this diagram shows that mains winding (each one) and the sense winding have a comparable number of turns. In practice, mains windings have 1 or 2 turns and the sense winding has 100 to 1000 turns. In the picture below, the sense winding and the transformer core are the black vertical component in the middle of the board. The mains windings are the white and black wire passing through the hole middle.