I earn money with Fortune Affiliates, for example, despite the absence of cookies. I would probably earn more, though, if cookies were in place along with sessions…
If I recall Fortune had that exit popup so I’m assuming that signups via the exit pop up are not credit to the referring affiliate.
Also If i remember correctly, with cookies if the expiry date is not set it is a temporary cookie that won’t be written to the cookie file. It will be forgotten when the browser is closed.