Indeed there was an AM F1 car, the DBR4, it was built when front engined F1 cars were still around, but got shelved as David Brown wanted to win LM, by the time he had acheived that goal F1 had moved on and the DBR4 was hopelessly outclassed in the few races it did.
There may be one at Donington, but there has also been one on track on and off for the past few years.
As an aside, David Richards is having a bit of a David Brown spell himself! Trying to win at LM and (part)owning AML, next he'll be moving into tractors.....