No because you're not using any data. And the carrier has data plans which you have to agree to ontop of your voice plan.
All you're really doing is using the phone as just a phone because you essentially turned off the data service the phone gets by disabling MMS & Data in the settings.
Essentially, they cannot charge you for data because your phone cannot send or receive any data due to turning off the service. Therefore making it just a voice only phone.
Reason being they charge by the usage [data plan or without]
Usage = Pay
No Usage = No Pay
This is because even though you have a smartphone, having the data turned off and never using it basically makes the carrier think its just a dumbphone - voice only and cannot charge you for using nothing.