If your SOP is great overall, they probably wouldn't even notice that They know that most people get a PhD to either teach or do research. As long as you conveyed passion in your field in your SOP (and not "I am getting a PhD because I don't know what I want to do in my life"), you will be fine.
I got the email asking for a list of professors I'd like to work with as well but did not get a confirmation that my application is complete, did you have to email them for that? Thanks!