@ampan - Do you think they'd have started the descent without it? They appear to lose it for a time, but it returns at timestamp 15:21. Unfortunately there are no publicly-available FDR traces to help confirm one way or the other (not that such information would likely be available on FDR traces of that vintage).
Both the Washington Transcript and the version from the Chippindale Report are downloadable as PDFs from :
Transcript
Note that while they make their position clear (the website being run by NZALPA), they at least provide a significant amount of the raw material from both the Chippindale Report and the Mahon Royal Commission for people to make up their own minds, which does them credit as far as I'm concerned.
The descent may have been VMC, but they tried to remain in contact with Mac Central, advising of their position and altitude as they went - remember that the crew were perceiving Lewis Bay as McMurdo Sound due to a combination of the track they were expecting to be on and the visual illusions that provided false confirmation. Perhaps they were expecting some kind of warning if they were off-course and even in the ATC transcripts (including those that were not heard by the crew), at no point did the radar controller try to warn them that they were approaching Lewis Bay and Erebus. If the transponder was coding at 15:21 - 26 miles east of where he was expecting it (which means that they probably did show up) - why? It's not like he was distracted by heavy traffic...
Because of the visual illusions and the fact that they did not receive any kind of warning before it was too late (in this case the GPWS) it is entirely understandable that the crew believed that things were proceeding according to the plan they had been briefed on because all the information they were receiving confirmed their mental model and nothing contradicted it other than a single-digit change that was not required to be checked against the flight plan they had based their work on the previous night.