They will probably make you take care of the negative equity (if any) as part of the loan process which should be easier in the early months of the loan. My impression of the process was that their only concern was that I qualify under their lending standards and only needed to finance 90% of the current value of the vehicle.
FYI, the total cost of my loan went from $30,000 to $22,000, so it's worth a try; my interest rate went from 10.35 to 4.15.