I understand being geek, but using oscilloscope to test a computer with ethernet/usb/other digital ports and HUGE internal state (RAM) is both ineffective and unreliable.
Instead of watching wave forms, you can connect any PC to the output port and run proper statistical analysis.
The established procedure (if the input signal is analog by nature) is to test system against several characteristic inputs - traditionally spikes, step functions and sine waves of different frequencies - and measure phase shift and variance for each input type. Worst case is then used in specifications of the system.
Again, if you are using standard ports, you can easily generate those on PC. If the input is truly analog, a separate DAC or simply a good sound card would be needed.
Now, that won't say anything about OS being real-time - it could be running vanilla Linux or even Win CE and still produce good and stable results in those tests if hardware is fast enough.
So, you need to simulate heavy and varying loads on processor, memory and all ports, let it heat and eat memory for a few hours, and then repeat tests. If latency stays constant, it's hard real-time. If it doesn't, under any load and input signal type, increase above acceptable limit, it's soft. Otherwise, it's advertisement.
P.S.: Implication is that even for critical systems you don't actually need hard real-time if you have hardware.