That sounds interesting.
But would it make sense for the females, specifically, to go out and hunt fruits and risk death, being physically unfit, and risk mating outside of their clan?
Remember, Kaguya was revealed to be able to bare children, so I'm SURE their reproduction roles are similar to humans, since well, she mated with a male, got pregnant, and bore children.
So your theory, is incorrect.
Edit:
It'd make sense for the males to seek fruit, give them to women to eat, and produce powerful, pure blooded ootsutsuki offspring...more powerful than kaguya, herself.
This actually indicates PLOT HOLES. Had it been a MALE, that was sent to search for fruit for the female alien to produce powerful offspring, being the one that mated with a female human(that died from complicated birth), then it'd save us the trouble of having to fill in so many blanks. You can tell, this "ootsustuki" origin and culture is far from complete. It'd do the franchise justice, had they started from THERE, instead. Kaguya should have been introduced at the beginning of the naruto series. Can't just throw in something of that scale, when it plays an important role in the origins of ninjas and chakra, at the last minute.
That alien story, is incomplete. And they need to thoroughly write it out, and figure it out...or just leave in limbo.
