If you can get the exception thrown only when another process has a particular state, or if that other process's state can affect the timing of the exception throw, then that's information disclosure.

Typically these are are hard to pull off, I remember a case a number of years ago where the proof of concept private key exfiltration came months or maybe even a year after the vulnerability was shown, and even then I believe the process took minutes or perhaps hours to run. This stuff isn't magic, it's really hard, but that doesn't mean it's not possible.