Not if you are using the tether function of the PlayBook. The PlayBook needs to have a wifi connection to use AppWorld.
If your phone can provide a wifi connection to provide the internet to the PlayBook, you will be able to use AppWorld when connected to the phone via wifi.
While we are at it, a lot of non Blackberry phones will not share internet with a PlayBook via BlueTooth tether, such as the new iPhone 4s. In the case of the iPhone 4s, the wifi hotspot works well with the PlayBook. My wife has even been able to RDP to her office using RDP on her PlayBook via the IPhone 4s hotspot.
This sounds good since I should be going iphone his summer.