I have not taken my NCLEX for RN but I have sent out resumes anyways, to get the ball rolling. I've had a couple interviews and I already have a LPN license so it kind of helps if they want to get the hiring process started. I just put on my resume that I am taking my test at this date. Good luck!!
I don't think it would hurt, but I wouldn't expect much. There are tons of employers who will flat out just say "NO" if you haven't taken the Nclex because they have tons of other people that did. So yeah.. I don't think it will hurt, but I think your search will be way more productive once you have passed Nclex.