My answer is: most likely, mostly. The Romans built their roads straight for three reasons: 1) This is the most efficient route for long-distance inter-city travel, as the shortest route between two points is a straight line. 2) They were built over largely flat land, so the need to wind up mountains or go around large hills was rarely an issue. 3) Flat roads are good for marching soldiers.
Add cars, and how does this change? These three points remain the same. But two might be added, if the Romans are smart. 1) Completely straight roads cause a kind of road weariness (some say a hypnotic effect) that can lead to accidents for high-speed drivers. If the Romans had discovered this, they might have built slightly curved roads, as the US did when building turnpikes and the Interstate system. 2) When roads were made of interlocked stone, rain water poured out between the cracks. Once macadam and asphalt were invented, it became a good idea to camber roads (to give them a curve with a rise in the middle, instead of a straight cross section) so that rain water would run off more easily.
The Romans were smart. If they had invented cars, they probably would have added a few curves to make roads better for cars.
They probably would have built roads a bit further into the Middle East, too. They would have needed gasoline.