The "draw over previous frame" is way better in flash. In photoshop for example if you have done like 50 frames and you want to change something in between you have to change it in every frame seperately - this is to my view a huge downfall. I assume you'd want to change a lot of things while doing the animation or maybe you'll miss something, that way you'll have this problem constantly.
For the gif you posted: yes but only if you have frames rendered already. The frames were exported from some 3D software like Maya or Blender and then put together as gif. Although I must warn you .gif only supports 256 colors so it's really hard to make it look good. There are ways to make it look better taken out of video format, but it will still be only 256 colors once in gif. I'd recommend exporing as something like .avi or .mp4 if you want to make animations like above.
Example of gif from motion picture format:
There's another way to get around in having more than 256 colors in gif but I haven't tried it out, ever. Theoretically you could divide your (unprocessed) frame sequence into several squares and add 256 colors to each of them. So it would take as many colors in each section as possible (if there's not more than 256 then the algorithm would compress), and if you sum all together you could get around 2000.
I haven't tried this tehniqe though for at least two reasons: I haven't found a decent software to do so; it would't take seconds to download the gif but minutes. GIFs can take a long time to download even in 256 colors (up to 5mb) but we're talking easily of 10Mb+ here, so it's actually like preloading a short video before watching it.
My conclusion is that gif is an outdated format which should better be left alone. You could do much better with simple video format.
Also here's my first Maya animation I did few years back and it was all exported as still images (frames) and rendered with Sony Vegas: