Hi Michael,
Yes, you can map an InfoPath form to a SharePoint list. There are two techniques:
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CAML - out-of-box, but somewhat complex to implement
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qRules - third party plugin (free trial), but easier to create/maintain
Qdabra has given free weekly webinars this year showing both techniques.
Here's one from last January showing CAML with a form that submits to a task list: http://youtu.be/4oQ7QdpYdx8
Here's another one using CAML from March: http://youtu.be/Fv-J8Qm4UeY
Here's one showing qRules: http://youtu.be/WftCp_EbcCU
Good luck!