In general the answer is no. Stage payments are usually released on the basis of value of work done, as opposed to the cost to produce that work. For example if you had done much of the work yourself in your spare time, you wouldn't have an invoice for the man hours spent?
We are getting stage payments for a build that is underway at the moment. What has to happen is our Engineer has to complete a buildings inspection report, which includes the value of work completed to date, this is the amount of the drawdown, based on what has already been drawndown, e.g.
1st report Value of work completed = 30k, drawdown = 30k
2nd report Value of work completed = 60k, drawdown = 30k, etc
You can draw down the value of the site even before you start to build. BOI allowed me to draw down the site value based on a valuation by an auctioneer. My engineer did not have to sign off on this. when I need to draw down the next installment my engineer will have to certify the work that is completed and the approx value to allow me draw down.