Can you hear a rattling or vibrating bass / guitar truss rod through your amp?

Quick demonstration of how a rattling truss rod is heard or not through an amplifier. Listen as the note decays and you can hear it. It's a really annoying sound. Many unscrupulous sellers claim that while the instrument they are selling has a rattling truss rod that you can't hear it through your amp or a recording. I beg to differ.

The amp is mic'd with a Shure SM57 to capture the sound.