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If WiFi is off, then the packet sniffer (i.e. Wireshark software plus whatever 802.11 hardware is in use) will NOT be able to pick up any 802.11 traffic from the device. However, note that you usually have a SIM card for connection that supports data over cellular; if this is the traffic he is able to capture, then turning wifi off won't help. I don't know of any capture systems for 3G/4G and the like that feed into Wireshark, but they may exist.
If it is 802.11 wifi in use, hopefully encryption is enabled with WPA2 which will make it harder to read the data captured.