Not exactly. A different board member got the first deposit check in first to get the first 'production' Model S.
But "first production car" can be a little squishy. Like with Roadsters, some VP prototypes eventually got sold, so a prototype could have been made before the customer production cars.
And they have done stuff with "Founders' series" cars being made in a parallel sequence to the regular production. And "Signaure" series.
I am not sure if they will have VP, Founders', Signature Model 3, or if they will all be "regular production".
In some ways there can be more than one "car #1". There can be multiple with a VIN# that ends ...000001 And Elon doesn't automatically get the first.
I suspect that key people are now trying out the RCs since the engineers have been working frantically to get them production ready, and key decision makers have to agree that it is time to start mass producing them.