Mine didn't.. Between two burnt plug wires, a terrible carb setup, and timing locked out at 35 degrees, it would drop 600+ rpm, and would quit with the idle any lower than ~1200. Coming to a stop would often kill it without two footing it. After addressing those issues (but before going efi), it would idle anywhere I wanted and drop ~100 going into gear. Nothing wrong with the converter.
While the converter isn't ruled out, it still sounds like there's enough unknowns and other issues that there's no definitive problem. If it is the converter, then when coming to a stop it would feel and act like a manual car brought to a stop without pushing in the clutch, which is a tough thing to try to describe. But coming to a stop real slow like could help identify it.
Heck, a video would probably do wonders to help pin things down. Doing the youtube account thing isn't that bad and could help clear things up fast..