This is impossible, no. Technically, not a single application works in the true sense, in the background on iOS. Fast application switching in iOS 4 means that some applications are still in memory when they are paused, but they can be unloaded at any time if the OS is required.
Applications can use a small number of background services such as background audio, VoIP, and location services. Each of them has its own API, so there is no way to request if any applications in the background use them in a general way.