The parts that interface with pins (sensors, LCDs, etc.) would certainly need to be rewritten, and might require a lot of work depending on what devices you are using in the project. Routines that use the standard C libraries could be reused.
Porting from the Arduino to the Beaglebone is somewhat easier, so if you haven’t committed to the Beagleboard as a platform, you might want to consider the Beaglebone instead. There are libraries for the Beaglebone that implement the most common Arduino I/O instructions (digitalRead, digitalWrite, etc), the most notable of which is Bonescript.
Dan.