Multiple desktops will not help you "stop clutter." They will empower you to spread the clutter around. What you really need is the discipline to take things OFF THE DESKTOP. Period, full stop, end of story.
This is what your Dock is for. This is what subfolders are for. This is what organization is for.
To answer your question, yes you can assign shortcuts to different desktops. But really, two or three folders in the Dock (Applications, Home and Downloads) is likely to be all you actually need to do.