FOR 12.04
If you're using 13.10 or newer see here..
Its possible...

As you can see the status section has been removed leaving just the Broadcast and Mail sections
To put a positive spin - open-source means you have direct access to the actual source-code. You can interrogate and change the code ... as long as you give back the code changes to others!
So here goes - the following demonstrates the code changes that are required to the package indicator-messages
prerequisites
Lets get source packages from the repository:
sudo apt-get build-dep indicator-messages
apt-get source indicator-messages
This will create a folder - name will change depending upon the package version of indicator-messages
. For 12.04 this folder is indicator-messages-0.6.0
code changes
Two modules in the folder indicator-messages-0.6.0
will need changing.
cd indicator-messages-0.6.0/src
status-items.c
Using your favourite editor add the line return NULL;
at or around line 80 in the function "status_items_build" shown:

messages-service.c
At or around line 893 in the function "resort_menu" comment out the code shown with /*
and */

lets compile
To compile this, move up to the parent folder
cd ..
Compile, make and install:
./configure
make
sudo make install
Logout and login.
to undo
To undo your changes:
cd indicator-messages-0.6.0
sudo make uninstall
sudo apt-get --reinstall install indicator-messages