Yes the dealer can place the order for the car earlier than your ‘official’ order date. I did it last year when I had my BMW 218i Gran Coupe. My date was 31st of July but they placed the order for the car in the middle of June.
Like others have said they will just order the car as a stock order then on your date they apply to Motability.
The danger of the car dropping off the scheme would be their issue, I would imagine they could apply to Motability but ultimately it would be the dealer that has to do the legwork and take the risk so I say if you definitely want the car, and due to the current delays all car manufacturers are having, then the earlier you order the bigger the chance you will get the car for your changeover date.
Hope this helps mate.