At least memory-intensive applications should be tested under such conditions.
When I was at college more than a decade back, I tested many applications under such conditions and my own application too. Most Microsoft's applications survived even with less than 100 bytes of RAM remaining and a disabled virtual memory! This included Microsoft Office, Visual Studio, et al. My own application survived too with a fix or two. Windows Explorer, funnily, crashed. Many non-Microsoft applications crashed.
More recently (2012), I tested two commercial Java profiler applications, JProfiler and Yourkit. They both survived without issues under such conditions.
