They can turn off everything they want in the plane. Radar will still identify it as a target, but it will not have the assigned code anymore or mode s code (denoting identity and destination essentially).
This whole situation is extremely strange and for the time being, I can only guess that the plane was blown up (no idea by who) or experienced some sort of extremely rapid depressurization which caused the plane to essentially disintegrate. As the plane was only 11 years old I believe? means it had limited reporting equipment that would have notified the airline or some sort of center if any technical errors were to arise autonomously ( I know this is the case for overseas flights over the Atlantic, though I am unsure of this for the particular airline and if the equipment would be mandatory for the flight under that route). The fact that the airline itself and nobody has any information that indicate something went wrong. The only assumption we can make is that it happened extremely abruptly.