Of course! If Yahoo! Web Analytics is unable to set a cookie, then it will identify the visitor as a first time visitor. The system can still retrieve information from the JavaScript tracking code, the IP address and the browser.
Cookie (HTTP cookie) = A small text file sent to your browser by a web server. It’s used for authenticating, session tracking, and maintaining user-specific information about users, e.g., site preferences, shopping carts contents, etc.