Depends - who are you pitching this product to? If you are pitching it to the consumer who is going to buy the car, you might want to rethink your business model, and if you are pitching just the product to a lender, you can forget it - all for the same reason. One of the reason car loans, like mortgages, work so well is called security - the car acts as collateral against the loan. In your product, there is no security 0- the customer has a check, but you have no way to file a lien against the title since once the customer has the check, your filing opportunity goes out the window. In a worst case scenario, the customer borrows say $10,000, prints the check (and btw, once the amount is printed on the check, it is no longer a blank check), takes it to the approved dealer (name on the check), buys a $2,000 clunker, gets $8,000 in change (dealer doesn't care, he is going to cash the check for $10,000) and never makes a payment. You can't repossess the car since you don't have a lien on it and even if you could, it's only worth $2,000 at best.
This is why lenders need all the auto information, etc. before they will cut the check for the exact amount.