Does Princeton want to see my resume?

“Hate” might be too strong a word. However with 27K applications, they certainly do not want extraneous documents. The instructions are straight forward. If you feel that there is some further details that need to be highlighted, write something. However, a resume where the AO has to read to wade through the duplicate info to find any areas that they think is what you want to highlight is probably not the most effective route.