I put $2,500 on my credit card (2% cash back!) when I bought my car, the most they'd let me do.
The variables that impact final purchase price (like financing vs paying cash) are one of the many reasons that the dealer model needs to just go away. Tesla is changing the automotive world quite a bit, and I'm hoping one of the things is people finally realize how obscenely stupid the dealer model and price haggling really is - and they have an option if they don't want to deal with it.
Ranting aside, no one can answer your question, since no one knows how they price cars. You could try just straight up asking, and then asking if the loan has an early payment penalty. The salesmen will certainly know you intend to pay off the loan early, but the sad thing is he won't care. He gets his commission off the sale of the loan, if that loan ends up making $0 in interest (and losing the company money in origination fees) he still gets paid, so if you and him "colluding" gets you a cheaper car and gets him a bigger commission he will certainly work with you.