You will never get a green tick if you don't have a Blackberry Data Plan. The green tick means that the Blackberry is accessing the BIS (or BES) server via Wi-Fi.
Without a Blackberry Data Plan you have to use applications that are Wi-Fi aware and don't need BIS access. You should be able to use the Hotspot Browser though apparently some devices are shipped without the necessary service records for the Hotspot Browser.
Why should you take the Blackberry Data Plan on your accout? Because it is far less frustrating using the device that way. The price of saving some money is doing extra work.
My other Blackberry is a PlayBook.