Only if you can find a bank that will loan on a vehicle that old and in that shape.
BHPH lots are in the business to sell to people that can't get financing anywhere. They sell older vehicles, usually junk but every now and then you will find a quality vehicle, then sell them for 3x or 4x what they have in them. Rather than charge interest, they jack up the price. As a rule of thumb, they ask for a down payment that is about what they put into the vehicle to recoup their investment. Then the payments are pure profit. If you have cash, ask the dealer how much he will take for the car as a cash purchase because it will be a lot less. BHPH lots tend to get a bad reputation, but then again, they often sell to untrustworthy customers who never pay.
While financing at a BHPH lot will not show on your credit report, many banks and finance companies will accept them as a credit reference. There are some national chain BHPH lots that will show on your credit (like Ugly Duckling, Drive-Time, etc.) and some franchise dealers who own BHPH lots and use those customers who pay good to upgrade to traditional financing later.