The technology must be there to record the data irrespective of whether the equipment is disabled.
It is, but not always selected as an option. When AF447 crashed, the initial cause of the problem (probe icing) was self evident as AF maintenance control in Paris were receiving the ACARS messages relating to the faults which triggered the chain of events real time. MAS hadn't opted for an maintenance data-link and weren't receiving such information.
However, Rolls Royce were. MAS pays for ''power by the hour'' which means that the engine parameters are relayed real time to the service provider. I suspect whoever disabled the ACARS didn't realise that the engine data was being transmitted by a separate system through INMARSAT which is why the first clue we had that the aircraft is probably no where near the last point of contact came from RR who were receiving data some four hours after secondary radar contact was lost.
My suspicions are that if the events leading up to this aircraft's disappearance become fully known, then a more comprehensive data-link system will become mandatory. I also suspect some form of auto-release Emergency Position Indicating Radio Beacon (EPIRB) will become mandatory. It's not beyond the scope of technology - my yacht has one!