I ran into this for the first time today. Not only was I getting iMessage and push notifications, Speedtest showed 0.11mbps downlink and 0.00 uplink. But at least some uplink had to be working in order to do the downlink test. Also, the Google home page came up in the browser, but I didn't try anything else.

I wanted to use email, but since I forgot about the www.unitedwifi.com page, I could not get the guard page to come up as it normally would when I went to any other site. Instead, it would just spin. So, I didn't even have the opportunity to pay.