Will my application still be approved if i cant prove dual nationality (non-chinese)

Hello! I wasn't really sure how to google an answer for this so I'm asking here. I'm applying to a university summer program in China and need to obtain a visa. On the visa application it asks to disclose any dual nationality. I'm an American with dual nationality in Pakistan. I seem to have lost my NICOP (national ID for overseas pakistanis). In the application there's space to give an explanation as to why I can't provide proof of my dual nationality. My question is, if I say that I have lost my NICOP, would this hinder the chances of my visa application being approved? Should I just go ahead and get a new NICOP? I'm worried that it'll take up to a month or more before I can acquire a new one.