This is how it could play out in a 777, if the 737 A/T system is radically different pipe up and I'll delete it!
The aircraft is on base and high relative to the G/P so the crew are in hdg sel with loc armed. Vertical mode is FlCh but App is not armed as they have not yet captured the loc (most operators SOP). The crew are concerned that an Alt capture may occurr at about the time of Loc intercept so they wind down MCP alt to either DA or runway, perhaps the raw data shows the ILS GP live so they are comfortable to do this.
Loc is captured but workload is high and the crew forget to arm App. At this stage the FD would be following loc in the lateral mode but an idle power descent to whatever alt was in the MCP window.
The crew now notice that the raw ILS data and the FD are in disagreement, its busy and they dont know why but opt to fly the raw ILS data.
On a 777 the A/T would make no attempt to control speed until the bugged MCP alt has been achieved, NOR WOULD A/T WAKE UP OCCURR.
The crew are so used to A/T ops with a good A/T that speed checking has assumed a lower priority in their scan pattern than it did when they flew previous types.
This scenario has ocurred several times on the 777, fortunately it has always been picked up before the speed got far enough below Vref to cause an serious incident.
Finally an apology if anyone has already suggested this, I thought I had read all the pages!