I am a B737-800 pilot now, but before this I flew the -300 and apart from the indicating displays, the system is the same.
You seem to confuse the workings of the A/T flight mode annunciation (FMA) and the thust mode display.
This is what the Boeing Operationaions Manual says in chapter 4, automatic flight:
With the A/T Arm switch at ARM, the A/T go-around mode is armed when descending below 2000 feet RA, with or without the AFDS engaged. Once armed the go-around mode can be engaged until 2 seconds have elapsed after landing touchdown.
This reflects the A/T flight mode annunciation. During the approach MCP SPD is active and GA will be armed below 2000 feet RA.
The thrust mode display indicates the N1 limit for autothrottle and manual thrust control and is normally calculated by the FMC. On the FMC N1 LIMIT page pilot selection of thrust limits is possible, but normally N1 limits are automatically specified by the FMC.
On an ILS approach, when the GS is captured, the thrust mode display indicates GA as the N1 thrustlimit. The Operations Manual doesn't say what happens on a non-precision approach.
One my flight tomorrow I will check the thrust mode display during the approach.
[ 31 October 2001: Message edited by: Mach .99 ]
[ 31 October 2001: Message edited by: Mach .99 ]