I think Andrew and Chris are saying that you normally don't need a comma after "etc." because "etc." is usually the end of a sentence. If you are putting "etc." at the end of a clause that is NOT the end of a sentence, then yes, you do need a comma. For example: "We bought various crafting supplies such as paper, tape, markers, etc., which we will need for the project." You can't omit the comma here.

I wouldn’t do that

No, you generally won't need a comma after etc.