rgbrock1...
You have posed a most interesting question.
In terms of the official investigation, with or without the recorders it will continue. As part of that, more research will be done into the aircraft's systems and equipment. More extensive analysis will be done on the recovered parts (these things are already being done, no doubt).
Two other points:
1 People think mostly of the recorders, but finding the main portions of the aircraft (even without the recorders) will be of immense value to the investigation.
2 In this day of private enterprise, and adventurers with buckets of money, I think (IMO) it is highley likely that someone other than the responsible "authorities" would endeavour to locate the aircraft if the official search is unsuccessful.
grizz