Yes Gayatri (Drashti) and Ranaji (Siddhant) would be driving and will not expect the other to come in each others' way. The actual reason, however, is because Ranaji would be driving distracted. He would be re-living the painful times of his life including the time when his wife died in a car crash and also his time fighting the war.
Ranaji recoveres before any damage was made and manages to prevent the accident from taking place. He takes a sharp turn and prevents the collision, yet again escaping death, as he says, and saving Gayatri and the others at the same time.
Gayatri, who has been desperate to get a glimpse of Ranaji manages to see him, even if it is just the side profile. Ranaji, will then say angrily that women should not be allowed to drive.
The upcoming episode of Ek Tha Raja Ek Thi Rani will have Ranaji and Gayatri coming face to face for the first time. Gayatri will be hiding in the royal library when they run into each other. Gayatri will almost fall flat on her face if Ranaji would not catch her in time to stop the fall.