We have a need within our company to use an online order form to keep track of sponsor purchases. Can the Marketo Forms be used as order forms with a running total of the amount due?
That depends on the information you collect in the form. Since Marketo is not inherently built as an ecommerce platform, the data you collect will not be secure and will be accessible by anyone with access to your instance.
It sounds to me like you would be better off using a platform like Stripe, Shopify, or Square to handle the purchases.
While it's a non-traditional application, it can work if the ecommerce platform has a nicely pluggable API. See my comments here.
But as Andy says, it may be more sensible to redirect the user to a dedicated cart widget (rather than trying to integrate such a widget tightly into the Marketo form). You have to be explicit about both front-end and back-end requirements: what needs to be in Marketo after the transaction, what's the ideal UX, etc.
Also, the question should be moved to Products ("Marketing Central" being more for discussions across the discipline as opposed to Marketo-product-specific questions.)