I asked a similar question to Tesla. In my case the CU will pay Tesla directly, not via me. However, in the event I don't get a signed MVPA until delivery, all they (Tesla) needs is some indication from, even if indirectly, the CU they will pay. In my for-instance I had a congratulatory email from my CU they would pay $nnnn against the purchase. Tesla said that email would suffice. I don't, honestly, think that would work, but if you got any on letterhead acknowledgement of the agreement to fund from the CU, that should suffice. Point to note: I counted and have purchased 15 (maybe 16) (only brand new) cars. Except for first car (~$2,200 72 Chevy Vega) I've used banks, financial institutions. I've never handled their check. Generally whether it's Cap One or Toyota Financial it's all handled by the finance person at the dealership.
What my bank wanted was a signed MVPA (not the unsigned one that was sitting in my profile on the website for weeks prior to delivery). This can be generated before you actually purchase the car. It contains the VIN, the total cost of the car, and a electronic signature from a Tesla rep. I got one via email the Friday evening before delivery scheduled on Sunday Sept 30 (last day of quarter). This created a huge problem, because my bank (a major US bank) refuses to wire money to Tesla or wire money directly to me.
On Sunday, I actually look delivery of the car with a loan approval and an electronic copy of my loan agreement. I'm not sure if this is official policy that is allowed everywhere.
What you need to do is press Tesla for a signed MVPA prior to delivery. It is possible. However, I did spend hours of the phone over the prior week, only to get the document on Friday evening 2 days before a Sunday delivery. It was surprising to me how it was so difficult to generate that document.
I have to say though, the car was well worth the hassle. Good luck.