Does MSFS log a system crash (not plane crash) and report it to ASOBO?

It doesn’t report the crash to Asobo.

In many cases, the crash will be logged in your WIndows Event View and you can see what module caused the crash. You’re expected to file a ZenDesk ticket with the information contained in the error log.

However, there are a crashes that don’t log the error at all. You get a mysterious CTD and there’s no trace of it in the event logs at all.