Yes having the diarrhea does flush toxins and bacteria out of your system.
When you're sick with the flu or stomach virus the diarrhea contains bacteria and toxins that need removed from your body.
Removal of those toxins and bacteria help you recover from the stomach virus or flu virus.
So while diarrhea is gross the diarrhea is actually benefiting your health when you have the stomach flu or flu or other illness.
The diarrhea is a good thing in those circumstances but you should still remain hydrated and replace lost electrolytes when you're having diarrhea as having diarrhea removes electrolytes from your body and dehydrates you.
But as long as you replace those lost electrolytes and stay hydrated it's a good thing when you do have diarrhea.