A Motability car sourced through a supporting dealer is exactly the same as any other lease. You sometimes pay an Initial rental for the car and you give up the Mobility component of either you PIP or DLA allowance. You need to have been awarded the higher rate of DLA/PIP, whichever one you receive, which works out to approximately £240 every 4 weeks. This money is signed over by the claimant to Motability operations who then lease you the car.
Anyone who has obtained a vehicle this was is every bit as qualified as any other leasee of a car to make a claim under one of the Diesel claims.
I personally have no idea if the claim would be successful or not, but any Motability customer is definitely eligible to make a claim.