Nope. Voice calls are sent over GSM, data is sent over (these days) LTE, 2 completely separate systems actually facilitated by 2 completely separate components in your device. Should be perfectly possible to turn the data transceiver off all-together and leave the GSM function unaffected, your device would still be able to send data over the GSM network (called GPRS or EDGE) but this would be incredibly slow, and also free on most contracts.
Conspiracy theorists are saying that the cell network operators have always pressurized/paid apple to prevent you from deactivating your iPhone's data connection, since they make SO much money out of it, especially out of teenage offspring running up huge data bills.
Just sayin'