Could the fire have taken out the voice side of the communications before or very shortly after the fire was discovered?
It has been suggested that there were other voice transmissions beyond those reported...
But to answer your question, yes.
ACARS data released could be the result of a section of loom being shorted... certainly, on the A320 family, the crew comms plug in just above the rear side window... given the list on the ACARS data, the looms to the comms and the windows may well follow a common route from the breaker panel/avionics bay... depends slightly on individual flight deck layout... one or two jumpseats, but the avionics bay is passively vented to the cockpit in flight and the breaker panel for the bulk of the avionics takes up the outer third of the cockpit bulkhead behind the right hand seat.
A hot and sudden fire would quickly overwhelm the suppression systems and give a very limited response time.
The Valuejet case highlights this... less than two minutes from initial detection of a hold fire to loss of power and control... especially when compared to the Swissair MD11 scenario... in that case there was around twenty minutes for the fire in the first class cabin ceiling to reach to cripple the aircraft