Is this true or not?

Old points distributors usually didn't like sitting energized without running. Using ACC was really important back then to not end up with points welded together

Ignition module being live and exciting the alternator are the two things that might be a draw. Doubt the ecu would be hurt by being live without a signal being sent.

Exactly. To the OP Cruiser: Yes, the transistor and related stuff is energized in the run position. your friend is correct. Some good, old style 70-80's boxes may not care about being energized in the "On" position. The crap, fake transistor boxes surely will fail quicker. My stupid opinion.

I run points in my Jeepster Odd Fire 225. I left the key on one day last summer by accident, it welded the points. Fact.