Since figs are inverted flowers, does it benefit the parent tree to leave some fruit on the tree to ripen/rot/fall off and be polinated during that cycle vice picking all the fruit for consumption?

Just wondering if it makes a tree more productive the following year if it is polinated the prior season.

Any research or experience with this?

Thanks 

I see no benefit for the mother fig tree by leaving fruit on its branches.

Had you been in a fig-wasp region; any (caprified) figs with viable seeds
could be eaten by some critter (e.g., a bird) and later pooped-out to
germinate into another (mostly useless) baby fig tree seedling...

Not in Maryland