Is flushing necessary when...

...you have used no fertilizers at all?

yeah, just dry and cure, only flush if you fert man. no worries!!!

well it could argued that it's not required at all. Though the smoke will be a good deal harsher and taste a little off without it.
I think the general ideal is that if you have gone to all the trouble to grow your own that you want the best possible experience from it.
...and yes flushing helps regardless.