No... I am pretty sure you cannot do this.
Icons that are not "pinned" to the dock for easy access are populated from left to right in the order that you launch the corresponding application.
What is in the dock is specified by the dock preferences file, and by managed settings (MCX) if the machine is connected to an Open Directory server.
If an application is listed in one of these settings locations, its icon will appear in the dock, whether the application is running or not. If it is not in one of these settings locations, the application icon _will_not_ appear in the dock until it is launched.
It is possible i suppose that there is a third party utility that is capable of what you are asking, but it is not something that the stock Dock in OS X can do.
Sorry... It sure would be cool.
Have you thought about using auto-hide on the dock...???
Set up your icons where you want them, and then set the dock to auto-hide. Then you don't see it at all, until you mouse over the edge of the screen... It's not quite the same... you would still have to deal with the clutter of icons while trying to switch programs...