The transponder light could only have come on once, being the occasion referred to in the transcript. Firstly, the radar's range was 40 miles or thereabouts. Secondly, the track, directly towards Erebus, was right in the middle of the radar's blind sector (see The Erebus Papers, p434). The only time the transponder light came on was when he went off to the right of track, on the first descending orbit.
If the descent was caused by the illumination of the transponder light, someone would have said something. What caused the descent, according to the transcript, was sighting the ground. Thereupon, he abandoned the radar assist and went VMC. If he assumed that his position had been confirmed by radar, he would have gone straight down, through the cloud base. No need to muck around with orbits.