Can the general public trace my IP address on FaceBook?

I have an anonymous guise on FaceBook which I use for my record collecting comments. I don’t want anyone to know my location, can they find my location simply by looking up my profile? I currently have nothing related to my address…

And trust me! I’m not being sketch or anything, I just don’t want the record labels to know who’s asking since I’m about 95% sure that I’m the only one from my specific city who orders all the time from these record labels and I don’t want them to put a face to the name.

Thanks in advance!