It depends.
Some carriers have multiple different types of data blocks.
For example, Verizon Wireless has a "data block" which simply blocks your internet. It doesn't block your app stores, picture messaging, etc. They also have a National Access Block which blocks ANYTHING that initiates data arrows. This would block picture messaging, app stores, etc.
Since AT&T Voice and Data services are closely related (as far as technology used) then I doubt they have an alternative to blocking all data. I have a feeling either you block everything or you block nothing.
Some carriers have multiple different types of data blocks.
For example, Verizon Wireless has a "data block" which simply blocks your internet. It doesn't block your app stores, picture messaging, etc. They also have a National Access Block which blocks ANYTHING that initiates data arrows. This would block picture messaging, app stores, etc.
Since AT&T Voice and Data services are closely related (as far as technology used) then I doubt they have an alternative to blocking all data. I have a feeling either you block everything or you block nothing.