If you don't bond neutral and ground at the main, it's still bound at the transformer.

> then the current will flow through the ungrounded conductor,

No, it will flow through the grounded conductor.

> back to the source (usually a transformer), across the windings, and eventually back to the breaker that controls the circuit

The flow of power is the same via ground as it is via neutral.

> This will build up enough current (usually VERY fast, like milliseconds)

There is no such thing as "build up enough current", current does not "build up".

The milliseconds has to do with built in time delays at breakers, it's not a function of the electricity.

> The Earth has nothing to do with this

The actual Earth is used as a conductor, so yes, it definitely has something to do with this.