Not exactly. The general term for the system that captures your first page is "captive portal". The short version is they intercept your first Internet-bound web request and send you a HTTP redirect to their login site. Once you give the portal whatever it needs to authorize you the local firewall is configured to allow your traffic out.

Generally captive portals will leave your DNS alone. They don't really have a lot of choice about this: if they poison your name cache you won't be able to get to your home page. Windows used to (still may) hold on to names for a minimum period regardless of TTL. A fair number of laptops have custom DNS. Combine those two and you can almost always get correct recursive DNS and frequently UDP 53 out.