Hi LoriDano,
No, the Tyros3 Firmware update V1.20 can NOT be installed on the Tyros4. Firmware updates are always model-specific.
With the update mentioned, certain USB WiFi adapters could be used on the T3. The T4 supports such adapters out of the box. However, nowadays it would do absolutely NOTHING for you to connect a USB WiFi stick to the T4: Originally, you could use it (instead of a LAN cable) to establish a so-called "Internet Direct Connection" (IDC) and visit certain special Yamaha websites from the T3/T4 (for downloading products from the former Yamaha download shop and for free downloading new Music Finder Records). These IDC websites were discontinued by Yamaha years ago. This Internet connectivity or a WiFi stick on the T3/T4 is therefore USELESS these days.
If you need a way to wirelessly transfer MIDI data to an iPad or Android tablet, I recommend a Bluetooth LE MIDI adapter (e.g. "Yamaha MD-BT01", "CME WIDI Master" or "Quicco sound mi.1 II").
By the way: The current Tyros4 Firmware is V1.10 (released in Jan 2012).
Best regards,
Chris