The Gertboard is not quite what you need. You need Stepper motor drivers such as the Pololu modules. Some of the electronics for RepRaps (there are many forms) come as arduino boards with added sheild (e.g. the RAMPS board), others merge the logic of the arduino into a single board.
This is then USB attached to a PC which runs either Java or Python or Perl code that takes the 3D model, slices it, generated GCode and finally feeds that to the arduino board that drives the steppers.
Getting the host code to run on the Raspberry Pi is not a problem. However the arduino code is running without an OS, running in real time and doing it direct from Linux is difficult unless you have a real time kernel and do lots of low level coding.
The other problem is that to run a RepRap you need a minimum of 17 GPIO output ports, 3 input ports and 2 analog ports, so replacing the PC with a Pi is no problem, but replacing the arduino board as well will be a problem.
The BeagleBone is probably a better match. It has enough GPIO ports, comes with analog ports, and has a subsystem called a PRUSS which is rather like having a build in arduino to do the real time bits. But even that will need a shield which has the Pololu modules and some MOSFETS (to run the extruder heater and the heated bed) on it.
However as I said above if you stick with the traditional electronics for a RepRap you can perfectly well drive that from a Raspberry-Pi using a USB connection - all the software runs well on Linux, and none of it will present any difficulty when it comes to using ARM versions.