Firstly my thoughts go out to those involved, not knowing is hellish, the sooner they find the aircraft the better.
Depending on the radar, if it broke up, ie simply fell apart then the radar image would show several returns which would be displayed for a while. It takes time to drop 35,000 feet, but does need a radar operator to see it at the time.
If it fell out of the sky, and broke up on the way down, then the first sign of a problem would be a sudden altitude change, followed by more returns as bits break off, again would need to be noticed by the radar operator.
The only way an commercial aircraft can disappear is if it vapourises or the transponder is turned off. Both would make it just stop showing on the radar screen, blink and miss it if you will...
The fact that no one noticed anything other than the radar signature vanishing is a worry. The discovery of one or more slicks suggest no fire, as kerosene is pretty volatile given the right conditions.
I suspect when the dust settles and the black boxes are recovered, they will show the transponder being turned off and the plane being put into a steep dive... 35,000 feet is plenty of time to issue a radio call if the flight deck choose to. It's interesting though that not one passenger was aware of an issue and rang or sent a text or something, although it was a night flight
The other alternative is that the flight crew switched the transponder off and flew to somewhere else,and that everyone is safe and well, albeit hostages. People are usually quite quick to announce such things though...