No, not really. The main reason is the Constitutional requirement of Secret Service. The Secret Service cannot protect the president if he just drives off nor is it easy or feasible to protect a person who is driving. The most that presidents have been able to do in terms of driving is to do in terms of driving is to drive a golf cart or if they are completely on private property to drive around that property. Even then the possibility of an accident is always a good reason for the Secret Service to limit the president's driving.
The late President Ronald Reagan, restricted from driving on public roads, enjoyed a pair of older four-wheel drive Jeeps on his 688-acre Rancho del Cielo near Santa Barbara, California, his home away from the White House.
"He'd be in the driver's seat and I'd be in the passenger seat and I'd have a death grip," from Secret Service agent Stephen Colo said.