Some carriers allow messaging, some may not. My carrier provides routine status updates on my data line, and as the iPad has no way of presenting these to me, I only receive them if the SIM card is in another device such as a USB modem or MiFi.
Back before T-Mobile became an official iPhone/iPad carrier. I used a data only sim with a Nexus 7/iPad Mini. To setup an online account, they sent a temporary pin to the device to verify the device. Since an iPad can't get these since they are basically text messages, I had to slip it into the Nexus 7 since they can receive those types of messages.
Of course now, setting up a T-Mobile account for a data plan does not require this.