Can you turn off Messages and still get iMessages from others? My daughter is constantly eating up data and uses Messages. I want that she does not get any iMessages until she is connected via Wi-Fi. 

Is there a option to turn off Messages when on the Cellular Network?
You can disable which app is using the most data instead. Some apps download data for updates, etc. For sure it's not the Messages app.

And for the Messages app, there's just an option to send an iMessage as a text message when cellular data is not available.

To know more, check this link from Apple.