Can I delete the "Cookies" custom page?

No, the “Cookies” page is “protected”, so can’t be deleted.

If you attempt to delete it, you will be presented with a message saying that the page is protected:

The “Cookies” page is used by the “Site Message” setting (Admin > Management > Settings > Other).

If the user acknowledges the site message, then it won’t appear on further page visits. The acknowledge_site_message path of the "Cookies" page sets the cookie that tracks the user's acknowledgement throughout their site session.