"Imagine the complexity as the current in one coil sets up a magnetic field which induces current in the next, which then..."

In theory, yes. In practice, a proper mic cable (two core shielded, balanced input at the amplifier) will not pick up enough even from an unshielded speaker cable to cause that type of feedback.
In a speaker cable, there are two internal wires carrying equal and opposite currents so there isn't the big magnetic field you imply by it being coiled up.

Triac-dimmed lighting, on the other hand, creates quite high frequency transients which leak out (and in) more easily. And GSM cellphones radiate a 200Hz buzz that gets in everywhere.

But this is all minor detail - acoustics are the #1 problem in a church.