WordPress.org

Can the signature option be overridden on the post/page editing screen?

Yep.

How is the signature included in my posts?

TinyMCE Signature will append your signature automatically to all your posts; no theme alterations needed.

You may also use the template tag tinymce_signature() in The Loop to return the signature.

Will the signature appear on an archive page?

No. If you want to do this, use the template tag, tinymce_signature() within The Loop.