If you refer to session cookies, the answer is no. WordPress won’t set any authentication or session cookie for logged out visitors.
But, keep in mind that session cookies are not the only cookies used and that WordPress core is not the only one setting cookies for your domain: in a normal site you have several plugins, themes, and third party libraries storing cookies on visitors browsers to provide a variety of features.
A great tool to see this is the browser dev tools (F12 in chrome).
See this capture for www.remarpro.com landing page https://ibb.co/gZ9R4U
As you can see, I’m not logged in but I still get some cookies stored. In this case most of them are used for Analytics purposes and set by Google Analytics JS library (you can’t avoid it, except you get rid of the library completely).

Hope this shed some light.
Take care!

Thank you very much. Upon inspection of the test site I have created for my client, as per your example, Google Chrome shows no cookies of any kind, which is great. If that changes when the real site is built and live, I’ll just nuke the GA JS and be done with it.