can we consider a customer estimate or take what a customer tells us outside of a formal financial statement as a number that can be used in pinpointing a gross annual revenue, even when we do not have documentation to prove?

You use the figure the lender used (the gross source of that revenue figure). If the lender didn't ask for financials, you can use the figure that the client put on their application, sure...but do be ready to answer why you take their word for their revenues over real documentation during your safety and soundness exam.