They can fail in either way; no spark OR no reference pulse for injectors to fire.
The module controls spark below 400 rpm. (Cranking speed, plus a bit more--but even at curb idle, in gear, the ECM should be controlling the spark.)
The ECM controls spark above 400 rpm, by sending a timing-advance signal to the module.
No RPM signal from module to ECM, no injector spray, and no spark, at least above 400 rpm.
Definitely a suspect but not to be replaced until actual troubleshooting is performed. If there's sufficient fuel pressure, and spark, but injectors won't fire - yeah, the most likely suspect at that point would be the ignition module. There are certainly other possible causes but you've exhausted the overwhelmingly common ones. One could troubleshoot further before replacing the module but you're reaching the point of diminishing returns there.
As a rule, the module failures take out the injector pulses AND spark.
On some trucks, you'll find the harness going to the module has gotten brittle so the wiring has gone bad.
Yup, that would do it, too. So many folks don't consider the wiring harness as part of the circuit.
Pickup coil in the distributor could be bad, too, and that's easy enough to test with a meter.
1. If the problem was the pickup coil, you'd have no spark and no injector pulse, because the module wouldn't have a reliable signal to trigger from.
2. Pickup coils can be tested with an ohmmeter, and the test can confirm the pickup coil is defective. The ohmmeter testing CANNOT confirm that the pickup coil is GOOD. Even if the pickup coil resistance is within spec, there are other possible failures that could prevent it from sending a proper signal.