If a line-in mic will amplify my voice over the computer speakers, why won't my wireless headset do the same? It interacts with the computer in all capacities except as an amplifying device.
Quite simply, because your computer's not been told to do it. While taking an input sound stream and outputting it somewhere else is pretty straight forwards, it still needs to be explicitly done, either with software or directly in your sound card. The fact that a wired microphone works while a wireless headset doesn't suggests that it's your sound card providing the loop back, as it gets the line level mic, but not the wireless one, which would be connected via Bluetooth or USB. To make it work, you'd need to download some software to take the input from the wireless microphone and output it to the speakers e.g. http://www.ntonyx.com/vac.htm.