That depends... Even on the local network I get lag on my Wi-Fi. Depends on if the data is sent in true (TCP/IP) packets or in a stream... If they are using Wi-Fi then it's not a steady stream. Normal transmitters I think operate on 2.4 GHz using streaming data.
There is an app (for iphone, not sure about android) that will do the same thing, but output a ppm signal so you can plug it onto your Tx. There is a free version that has 4 axis, one joystick and 2 accelerometer. Its called flypad.
It is not the packet nature of the communication or the handshaking used in the medium but rather the bi-directional communication on a simplex medium which is shared with as many users as are in range of the AP. Co-sited users on the same AP are the real concern for communication reliability.