"Does the existing hole have to be widened and deeper-threaded for the coil to have something to sit in, and have thickness, and provide pedal threads at the original diameter?"

Yes. A larger hole is drilled concentric with the damaged threads and a special oversized tap is used to make new threads. Then the insert is inserted with a special tool, which compresses it to a slightly smaller diameter to twist it into the threads. The insert then expands to lock itself into the hole.

A good machine shop can also do the work, especially since it is the right crank arm with a right-handed thread which is more common; left-hand threads are pretty bike-specific.