No. No addresses, no names, no fingerprints, nothing that follows anybody anywhere.
What is kept is which page was asked for, how many times, and the page that linked to it — which is a page rather than a person. The linking page is kept without anything after a question mark, because that part can carry a key or a tag that belongs to one visitor. On a site with plain permalinks, the part that names one of your own pages (?p=12) stays. Nothing leaves your site.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.
