I have to chime in on this one, because I speak from experience.
I spent a week at the lake, and not wanting to run to the grocery store for meat.
I found honey locust with some sweet looking saplings, less than 2'' across.
I Wacked several off and and began profiling with Obsidian.
after a few hours and some heat treating over a camp fire, I had a serviceable 45# @ roughly 28" draw.
This is a plausible and very effective option, even in a short term scenario.
You don't need a work of art to procure food, you just need to maintain three goals.
Form, Fit and Function
You would be surprised how many critters come into range while you are hacking out a quick bow around a camp fire.
But keep in mind, I did have bow string already made up. I always carry several Pre made Bow strings in my Bug Out Bag.
If you have not done this, then I urge you to Test your self, before the situation presents it's self.
Just my two cents