Yes, if you have the wifi logo in bold then that means that BIS is connected through wifi and all that data will go over wifi. Any app that will connect through BIS will work over the BIS wifi connection. Most apps made for the BB work over a BIS connection.
If you have a BB data plan, then set the browser for Internet Browser. It will use the wifi BIS connection first. If you set it for Hotspot browser then when you're not in a wifi area, you won't get anything using the browser.