The combined crank / cam position sensor on older NSXs always looks like it is ready for the junk heap because the potting compound starts leaking; but, I have never heard of a confirmed failure. The sensor is a dumb-ass simple device consisting of four passive reluctance type sensors. The test for the sensor is set out in the service manual and just requires an ohmmeter. Other than the access issue the test is easy to do. If the sensor passes the test it is theoretically possible that the sensor is damaged and it still passes the resistance continuity test (coil pole mangled or some weird thing like that); but unlikely. If one of the coils on the crank sensor is completely out, I am not sure that the engine will start.
The ECU uses the crankshaft speed signal to detect misfire codes. It is typically a one or two trip type fault to trigger a display of a misfire code. On some Honda ECUs if you are clumsy with the clutch and do a repeated stop - lurch - stop - lurch you can trigger the ECU into generating a false cam / crank sensor failure code. My son did that on his 2005 RSX once when he first got it.
Short answer, no sensor error codes, the engine starts and runs without shaking like crazy or really down on power (running on 3 cylinders) and the four coil resistances values match the service manual values I think your problem is someplace else.
Edit: If you do the resistance checks on the 4 individual sensors, wiggle the wires a bit while doing the measurement. Watch for fluctuations in the resistance measurement while doing this which would indicate a flakey electrical connection. If the sensor is going to fail chances are it will fail via a broken wire where the wire enters the body of the sensor or a broken wire / bad connection at the plug. This could be an intermittent fault that is temperature or vibration sensitive and an intermittent fault might mimic a misfire depending on the algorithm that the ECU uses to detect misfires.