Will Google's Third-party Cookie Restrictions Affect Athos Commerce on My Site?

In short: No. 

Google Chrome has rolled out restrictions against the use of third-party cookies in the browser. However, this is not a new concept, as browsers like Firefox and Safari have already been doing this for several years.

Since Athos Commerce holds its cookies on your site's domain, they are not considered third-party and are therefore unaffected by this change.