The iPod Touch does not have a built-in microphone; but it does have a microphone input pin on the dock connector (some VOIP apps using the plug-in microphone connection allegedly work on jailbroken units).
The official iPhone SDK API does not seem to allow developers to use this input. I did actually try plugging-in one microphone and but found zero sound input data. So a recording app will probably run on an iPod Touch, but all you'll get is silence.
Not sure why Apple doesn't allow developers to use this input pin on the dock connector. Try writing them and asking.