I don't think you can relate the trans to a VIN. On the driver side of the case is the casting # that includes the date. On the passenger side is a tag which identifies the trans, copy attached.
I have looked around a bit and cannot find any info to link the trans to the vehicle. There are several 4R70W transmission cases, some have two bolt starters and others have 3 bolt starters. So ensure you have the one that matches your car. I think you will be relying on the integrity of the seller that the trans is in good condition. A warranty is good, but there is a lot of hassle as I found out.