You scared me for a sec, but looks like this isn’t the case. When I got my 3P last year, I put a $100 deposit down and they matched me with a car, and the formal agreement was drawn up. This car was delivered after 3 days.
The order agreement and the purchase agreement are dated the date of the deposit. Actually the order agreement and the purchase agreement are the same document, just with a vin and finance docs attached.
The order agreement with the $100 deposit actually has the header “motor vehicle purchase agreement”