A runner continuing to run and drawing a throw may be considered a form of interference. This does not apply to the batter-runner running on the dropped third strike rule.
Would continuing to run after being out apply.
Continuing to run and drawing a throw after being out is a form of interference and the runner closest to home would then be called out. But, this does not apply to a batter running on a dropped third strike if that is what you are leading into.