If you book it in well in advance and they have an auto available, yes they do. However, they should come and collect your car and drop it back to you for free. Alternatively, if you are in no hurry and it is a quick repair, you could wait for it?
I have only once in the 20 plus years using motability that I have had to take it to the dealer and wait for it.
Current car 2019 Ford Kuga 1.5T Titanium X Edition (White)
On order new Vauxhall Grandland Ultimate 1.2 Turbo (Ruby Red)