If you're asking whether Outlook must be running in order to function, that
answer would be yes. I don't know of many programs that function when they
aren't running.
Receiving mail offline makes no sense to me. What does that mean?

How would any program do anything if it wasn't running?  Sure would make
using Windows a lot faster to use if you didn't have to load it.  Bill makes
lots of money but as yet he hasn't been able to capture the magic needed for
future events to occur in the past which is your present.

Yes, obviously SOME program would be needed in memory so it can run to then
perform the functions necessary to e-mail.  That could be Outlook.  That
could be some mail monitor utility.