Michael:

By budgets I assume that you are referring to Job Estimates. The Direct Job Analysis report will likely be what you are looking for,

Needs to be better stated as I don't understand exactly what your expectation is. "Can we input quotes directly into job cost and have invoices in AP draw down against the quotes when we key in those invoices?". There is no quote process in Job Cost. Basically when you invoice jobs the invoice amounts comes across to Job Cost as a billing and you can compare the billing amount to the contract price.