Compiling C++ on EFM32 microcontrollers
Of course it is possible to use GCC with a Cortex-M3 chip. (I assume the manufacturer has not deliberately kept something secret that you must know in order to do so).

In a nutshell, you must


get or write startup code (ctr0)
get or write a linkerscript
find out what special command line options you need (-nostartup etc)
find out how to download the application (probably as .hex file)
(optionally) write a makefile to automate the process


If you use any built-in libraries or code generation tools of the IDE you'll have to port that too.

As a start, check out any project that has combined GCC and EFM32. RTOSses like FreeRTOS and uCOSII are a good place to look. In a comment markt suggest coocox, also worth a look. It is much easier if you can start with a know-working set of scripts and make your own one step at a time. 

Been there, done that, but for the NXP LPC1114/LPC810: check www.voti.nl/bmptk At the moment (december 2014) I am reworking it, but the .zip should work and can give you an idea of what is involved.