Digital marketing companies are moving to reduce or eliminate their dependence on cookies for identifying users, so unless they add some Tor-like functionality to this tool that makes you appear to be connecting from a different IP address, I don't see this having much of a long-term privacy impact.

That said, no need to volunteer any more information than necessary to use online services.

If you haven't seen it, you should definitely check out https://panopticlick.eff.org/