Short version:
Yes, the radio altimeter did not function properly, and played a role in the particular sequence of events that happened here.
However, from the evidence so far available, the crew's behavior was such that, when combined with any number of other minor faults, it would have had precipitated similar or worse catastrophic results.
I also find bewildering the number of self-professed technology experts who, when presented with a problem involving the unexpected interaction of three components (radio altimeter, autothrottle, autopilot), think the solution is to make the system more complex and further isolate the operator from reality.
A perfect "RADALT1 failure detection system" will not avoid future tragedy if pilots forget to fly the plane.
At least that's the case to my untrained eye.