All which is said below is implementation details - FOR WINDOWS - and mostly undocumented behavior. Do not rely on any of the information.
As an implementation detail, this task will most likely be scheduled to execute on a thread pool thread.
If the task has not started by the time the process exit starts, it won't matter it was queued in the first place.
If the task is currently executing, then according to some of the implementation details of process shutdown on Windows eventually only one thread will be executing which will not be the one executing this task. So, it will be forcibly terminated in that case.
If the task has already finished execution, whether through completion or by throwing an exception then there's no thread occupied by it. However, if the exception was left unobserved then the finalizer - should it get a chance to execute - will throw that. Please note that finalizers are also not guaranteed to execute under any circumstances.
This page should have been visible, but Microsoft's latest screw up in revoking access to old MSDN blogs continues.
Similarly, if you can manage to track the first link on this page then do so and read it.
P.S.: Here's the link for Raymond's blog. What you'll find from both sources is that only one thread continues the process shutdown.