Does putting an iOS device into single app mode prevent iOS upgrades?
We block iOS updates via different ways on our iDevices:


Via our Firewall, you can block these URLs on your WiFi network : mesu.apple.com, appldnld.apple.com. 
Or you can block WiFi network on your devices via restrictions in a profile pushed by your MDM. So devices will be not able to download iOS updates, but you need to use only 3G/4G.