I'm in a similar situation. The application I'm working on does not ask for a resume or CV, but it does allow for the upload of supplemental materials. The wording on the application makes it sound like you should only upload something if the department specifically asks for it, but there is a lot of stuff on my CV that cannot be included in what is asked on the application, given my non-traditional situation. Another issue is that the application only allows for the required 3 letters of recommendation, but the department I'm applying to does state a fourth can be submitted. In general, departments specifically say they are not interested in non-academic/non-research-related recommenders, but since I haven't been in school for years two of my letters are from profs I haven't worked with for 11 years, and the third I haven't worked with in 7. I'm wondering if a letter from my current employer, the headmistress of my school, might be helpful in that it's current, even though it is not research-related. I am currently waiting for a response to an inquiry email I sent to a prof in the department I'm applying to, and assuming the response is favorable I'll follow up with both these questions. I'll let you know how this goes, but my advice would be to do the same. Establish good contact with someone in the department and then ask them if the resume would be helpful. If it doesn't add anything to your application and it isn't asked for, the response will probably be no.