No. It doesn't work that way in tablets. That wouldn't be legal. They can make it so you can't access 'data' if you don't have data through whatever carrier/service provider you use, however they can't restrict the WiFi access.
You can try taking out the SIM, however in some devices they won't work if the SIM is removed. If they have something on their SIM that restricts WiFi access, that would also not be legal. And more so if you no longer have any service with that carrier/service provider.
You could also have an app that is interfering with it, but that is also less likely to effect this. If it doesn't' work, it may well be hardware.