Yep, they'd give it up. Let em figure out how to prepare all that bug infested, nutritionless, stale canned food that's been in the basement for 40+ years. Most would be glad to get rid of it.
I gave my daughter my wheat grinder (which I haven't used for decades), and now have a storage can of wheat already ground to give her (in case she wants it).
Cleared a lot of storage area in my cupboards.
Also, decades ago, I tried to get rid of containers of stored wheat I had in my garage in large plastic containers--even donate it to anyone who would want it--but no one raised their hand.
I customarily backup my food reserve to cover three months. I use from this and replace what I use so that it is always fresh enough to use. To store huge amounts if food, in my opinion, is an exercise in stupidity!!!
Many would dutifully hand over their entire supply trusting it would be fairly redistributed. Of course the elite would get the best while everyone else would get the rotted out of date stuff.
I think a large number would give a token amount.
There's a huge difference in faith that the system will protect you and knowledge that you are already protected.