Does Chase say you are approved for x amount, say $40,000? You take that to the dealership and they turn in the final price to Chase for the loan to begin?
I've only done it once, but yes, that's basically what happens. But I wouldn't take the amount to the dealer and tell them that's how much you have. I would just tell them you have financing taken care of and negotiate the price from there. This is what I did...
I test drove a few cars, researched online and shopped around a little in person over the span of a few weeks. Once I knew what I wanted, I figured out exactly how much I needed to finance based on my down payment (you could presumably do this by estimating fairly close to what you could expect on a trade-in), and based on the price I was willing/expected to pay on the car.
When I knew how much I needed, I added a little bit to it for a buffer and then went to Chase looking for that amount. They pre-approved me for that amount and told me they would cut a check directly to the dealership for the exact amount once I found the car. I had approx 30 days to find the car.
I called a bunch of dealerships all over the south and found the car somewhere out of town for 10% less. When they asked about financing, I told them I already had it taken care of and that I would basically be paying in cash in the form of 2 checks (1 from myself and 1 from a bank). Got the dealer to write up the paperwork and send it to me and the banker. I did the paperwork I needed to for the bank, they cut the check, I took a ride to the dealership, hand delivered the bank's check and my check and drove the car home.
TL;DR - had only $10K, wanted $25K car, got approved at chase for $15K, found the car for $22K, Chase cut a check for $12K and I picked up the car.