No, you can drive it. I did. I camped in Saint Mary's Campground, the eastern most campground on the east side that is just off the Going to the Sun Road. It was a very nice campground and I was surrounded by huckleberry bushes that were loaded with ripe fruit. There is another campground further along the road going west, but I recommend the one I stayed at. You can make reservations, but I arrived without them. Fortunately, there is a commercial campground just outside the park that was very near and I stayed there the first night. Then, I was able to get an unreserved site the next day.
I'm including a picture of a very scenic spot early on the east side of the Going to the Sun road. This isn't one I took, they are on my other computer, but I have this one in my wallpaper folder. There's fairly limited parking here, so it pays to get there early - and, the water may be calmer with beautiful reflections.
There are other scenic views along the Road too, but this is my favorite. The little island was caused by a landslide from the slope on the right, quite a long time ago I guess.
The waterfall hikes I mentioned are near the Saint Mary's Campground too. I'll try to post some more pictures in the morning.
- Jack