I had the same question as you because I am working on a small laptop with limited screen real estate, and I configured my touchpad to perform all of my workspace switching. I found out how to remove the icon, and it is not too involved. Please note that I am using 12.10, and this may not apply to 12.04. I am still a novice programmer and linux user, so please excuse me if I misuse any terms. Since the workspace-switcher-icon AKA the expo icon is "baked into Unity", you have to get the source code, alter it, and recompile it. The procedure is very similar to the one mentioned here:
How can I disable arbitrary default multitouch gestures in Unity?
Here is the procedure:
In terminal, enter these commands:
$ sudo apt-get build-dep unity
$ cd /tmp
$ mkdir unity
$ cd unity
I used the tmp directory, but you could do it elsewhere.
Get the Unity source code:
$ apt-get source unity
Go to the directory "unity-6.12.0":
$ cd unity-6.12.0
Use your text editor of choice to open "LauncherController.cpp"
$ gedit /tmp/unity/unity-6.12.0/launcher/LauncherController.cpp
Press Ctl+F and seach for "workspaces". On Line 627 there is a command
bool wp_enabled = (workspaces > 1);
Change the "1" to a higher number than the number of workspaces you wish to use. For instance, I want to use 3 workspaces so I changed my entry to look like this:
bool wp_enabled = (workspaces > 4);
Save and close the LauncherController.cpp file, and then build Unity:
$ dpkg-buildpackage -us -uc -nc
It will take a few minutes. Then install the modified Unity that you just built:
$ cd ..
$ sudo dpkg -i *deb
Once it's installed you logout and log back in. Then open CCSM, go to General>General Options>Desktop Size tab, and change your number of desktops to 1. You should see the Workspace Switcher icon disappear from the Launcher. Now you can change your number of desktops back to the number you want to use, and the Workspace Switcher icon should remain hidden. You might be able to reboot and accomplish the same result, this is just what I did. You're done!