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It will depend on the individual hamster to some extent but I've never has a problem with them burying fresh or wet food in their burrows or hoard, all of mine have tended to eat what they want out in the cage & just leave what they don't want. I have had small pieces get lost in the substrate a few times but they do tend to just dry out so it hasn't been an issue.
If your ham does take veg into the burrow or nest you can just check it every few days to see if anything needs removing it shouldn't do any harm if it's in there for couple of days.