I usually create my icons and illustrations using GIMP. I'm sure everyone who uses GIMP knows that it pixelizes the images so when you get shapes that curve or are round, the edges appear jagged. I concocted a theory that, if I create these icons/illustrations at a high resolution (say 5000px +) that the jagged edges will appear less? is there some merit to this theory or am I just full of it? I would like to, finally, put this doubt to rest and to know the truth from someone who really knows
It has to pixelize because the screen is made out of discrete pixels. To combat this is anti-aliases the image. Now there are many ways to do anti-aliasing. In essence you have a trade-of between ringing (to sharp) and blurring, and implementation factors such as speed memory consumption etc.
Now, there is some individual variation as to what anti-aliasing strategy you consider making a good result. It result is also affected by the display your using your mood, ambient color of the room, color calibration and what you were doing before you looked at the icon.
Now is it possible the rendering a big icon anti-aliases better? Yes, its possible. The typical vector graphics rasterizer is optimized for speed. They also often have a conflation issue (bug) that is caused by using coverage computation as alpha source and then alpha composing the image.
Image 1: Art optimized done in Illustrator (left), and linear Lanczos filtered (right)* see more discussion about this here.
This is a trade of however, you need to know what your doing and you lose control of the pixel values. So at extremely small scales it starts to work badly. Many icons have this property so it is not a universally good strategy for all cases.
If you design your icon or illustration or whatever it is at 5000 pixels and view it at 5000 pixels then you will have smoother curves, lines etc. Yes.
But. If you, for example, need a 32x32 pixel icon, design it at 5000x5000 pixels then reduce it in size to 32x32 pixels (or simply view it at 32x32 pixels) then the result will most likely be worse than if you had designed it at 32x32 pixels—Because you're relying on something else to do the reduction and decide what pixels fall where on the new pixel grid.
If you're intended output size is large then working even larger isn't really a problem but at small icon sizes it's best to have complete control over each pixel rather than letting some resizing algorithm decide what goes where.