No, Beejive does NOT have fast-switching enabled. It hasn't been updated for 4.0. It was released on June 8, which is before the App Store started accepting 4.0 apps.
Before fast switching, Apple encouraged app developers to have their apps save their state on exit, and restore it on start. Unfortunately, this didn't catch on in the developer community as well as Apple had hoped, and this wasn't a "must" for acceptance to the app store, because there are some types of apps for which this wouldn't be appropriate. As well, many developers implemented this poorly or inefficiently, with some apps taking 30 seconds or more to restore their state. (Navigation apps are notorious for this.)
For apps that have implemented their own state-saving, the only difference users will see when/if the developer implements fast-switching is that perhaps the app will seem faster to restart. It's confusing for users because the task bar really isn't a task bar - it's a "most recently used" bar.
In 4.0, the OS can save the app's state for it, in a very fast and efficient way. But the app does need to be updated for 4.0 for this to happen. Apps that save their own state can still continue to do this on devices that don't have multitasking support. (3G and earlier, and devices that haven't been updated to 4.0.) That is, updated apps can do both, depending on the device they are running on.
Beejive obviously did everything right in the pre-4.0 world. I'd expect it to be even more fabulous once they update it for 4.0.
(I do not use or have Beejive myself. I'm a developer, and am only commenting based on what I have read here about Beejive. Since I'm a developer, I'm able to read between the lines a bit.)