Yes, you absolutely can! Most major driving institutes like Excellence Driving Center allow you to open your file and register for a driving course entirely online without needing to visit a branch.
While you can complete the paperwork and registration online, the RTA mandates that you pass an approved eye test before your RTA traffic file can be officially opened.
You don't necessarily have to go to the driving school's branch for this; you can visit any RTA-approved optical center (like Yateem Optician, Magrabi, etc.) in a mall near you. They will upload the results directly to the RTA system so the driving school can proceed with your file.