You mean Bank check, right? The one you get that gets drawn on navy federal and is for initiating your loan with Navy Fed, that has a spot where the VIN number goes, and a process Tesla needs to follow to process it?
I bank with Navy Fed, and both my tesla loans have been through them (navyfed), but I handed the bank checks (the name for that type of check) to Tesla directly, when I picked up the car. When I handed it to them when I arrived for my delivery appointment, they (Tesla rep) went away for 5 minutes and came back and told me I was all set.
No idea how long it takes if they process it by mail though. Might be a good question for whomever you are communicating with at Tesla related to your vehicle delivery / pickup.