Connecting to a tower specifically (blinking green) doesn't actually consume data, however other parts after that in the process do.
Under ideal situations, a session resume can be done, which uses less than 200 bytes of data. This is also the overhead when waking up from sleep with cellular off.
There can be overhead for sending things like device vitals, which do not consume data operations but do use a small amount of data.
Under worst case conditions, repeated failure to connect successfully could cause a session invalidation, which would require up to 5K of data to authenticate with the cloud again.