If it's in your deposit contract that you would allow such a thing, but then how do you make the assertion that your contract is legal when it's signed by a minor? That sounds sticky. As the legal guardian of the minor, they may have some rights, but that's probably state specific and nothing I'd want to comment on.
Sounds like it might be something you need an opinion from legal counsel on. I personally can't come up with a way this would be enforceable. Why not just have it as a joint account to at least make sure you're covered and have a contractually liable individual? I know that's not your question, but it seems like you're opening yourself up for issues that could be avoided fairly easily. Why does marketing want these to specifically be individual accounts? I guess that's the question I'd be asking.
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Someone's about to get horned!