"Unable to send email" error shown to anonymous users in Workflow action
I'm assuming you're using a Rules Event "Before saving content (optionally limited to selected content types)", or some variation of a node related Rules Event.

Try to add a Rules Condition like "Entity has field" (related to that node:field-email field). After you do, that field will be available as a token you can use in any subsequent Rules Condition and/or Rules Action (where a field of that data type can be used). Your 2nd paragraph appears to me like a confirmation you don't have such Rules Condition yet (so Rules has no clue you're interested in using that eMail field).

With that, you should be able to just get it to work with the Rules module, due to which your "note" probably doesn't apply/matter anymore.