This is exactly what I did. I financed through Tesla, kept it simple, put minimum down (taxes/fees only), and then when I had my Tesla loan, I paid the remainder of my intended true "Down Payment" into the Tesla loan, and then just re-financed into DCU for 65 months @ 1.24%.
DCU won't charge any fees, nor most major lenders, but I did see this in my Tesla Finance agreement:
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I was not charged anything with US Bank (My Tesla preferred lender I guess), but you should be able to confirm with Tesla/Lender prior to taking delivery. I don't know if this refers to making a payment before it's due, or if it's referring to early pay off. This looks like standard lender language to me though.