As to overrides, if your YOUR_TEMPLATE folder has a "jscript" folder, then all lookups to template_default for "jscript" files will be completely ignored, and only your YOUR_TEMPLATE/jscript folder will be used.
So, it's quite possible that if this plugin relies on such files then yes you'd need to put those into YOUR_TEMPLATE instead of template_default.

But strictly speaking, for all the "sidebox" files (module and template), you don't strictly have to use an override folder, if you want the feature to apply regardless of which template you're using.