Doc -
It is totally possible. I think it could be an excellent project for a group of students, because it is readily divided up into separate pieces that allow for quick "first-success".
First, tie all the ground lines to your arduino. Pull 5V from the DSC to power the arduino - there isn't a line for this on the 37pin connector, so pull it from one of the spare 5V pins (there are tons of them).
I would not recommend having the arduino connected to a computer and the robot at the same time. Arduinos aren't well protected, and it is easy for a student to accidentally dump 12V across something that doesn't want it.
Next, enable /Output_EN by pulling it low with a pin on the arduino. This enables/disables all of the pins that make things move.
Then try sending some PWM signals. There are lots of threads on this board about the times for these. Quick summary - 1.5 ms for stop. Jaguars are .66ms for full reverse, 2.33ms for full forward. Servos and Victors are 1ms and 2ms. Off period is pretty forgiving.
Then try using specific sensors with the GPIO. This will be different per sensor.
Save the shift registers for last. These control the relay outputs and some other (largely useless for your purposes) pins.
I wouldn't bother with routing I2C through the DSC. Just do it raw through GPIO.
PS: This is a bit embarrassing, but I just saw that the 2010 pdf export missed one of the pages of the schematic! The Altium source files include it, but somehow it got lost in translation. The 2009 pdf has it :
http://usfirst.org/uploadedFiles/DSC...matic%20v7.pdf