I have tried this and it does not cause the issue to happen. When the issue is happening, pressing the brakes appear to be the action that causes the result, but when the issue is not happening you can pump the brakes all you want.
This is my understanding as well. I'm not seeing any vacuum lines from/to the engine, but rather a separate electric booster providing what I'm guessing is vacuum. I'll admit I have like 5% understanding though so I am lacking info at the moment.
Just getting back from a work trip, and we will be running around in another car today so we don't get stalled, but hopefully I'll have time to take this out and see if I can get it to act up again in the near future.
When it was acting up last week I checked the battery voltage while it was running and it appeared that the voltage was around the 12.7 mark meaning no alternator supplied voltage going on, but it jumped back up to 13.7 shortly after so I'm not positive if it was an issue with my voltmeter or if it was actually reading 12.7 for that quick check. That's what I'm currently waiting to check again, but I need time to drive it around and wait for the issue to pop back up to check.