Yes it would, a screen replacement for the iTouch 4th gen is the digitizer glass ("touch screen") and the retina display fused together. No regarding your WiFi how did the iPod break in the first place? Water? Drop? I would try restoring, and if you are experienced enough when inside your iPod check to make sure all of the cables are properly connected.
Parts can be found on eBay and I think iFixit has parts for the 4th gen also. If you buy from anywhere other than iFixit, remember DO NOT buy the LCD separate from the glass or vise-versa.
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