SMS is not a data protocol, it's a telecom protocol*, so you certainly would not receive an SMS through a wifi data network. You have to have your telecom service enabled in order to receive an SMS.
There's usually no reason why you can't activate your telecom service while OS. Enabling your mobile data service on your mobile device OS is a different issue, of course.
Needing to receive SMS messages is almost the main reason I ensure I have my Aussie SIM in a device while overseas. Phone calls can be diverted or sent to Voicemail, and other data services can be replaced (e.g. using wifi hotspots), but SMS messages can't be diverted, and expire if they are not delivered within a certain timeframe.
It's also another reason why using data-based messaging services, such as iMessages or Whatsapp helps to overcome some limitations with SMS, though of course (as you've discovered), these services don't help when you actually need to receive an SMS.
*I'm using these terms broadly to distinguish between services over telephony networks, including mobile telephony v. computer data WAN/LAN/Wifi networks