No, the headers on the kit fit on an Arduino or compatible but not a Raspberry Pi 3. Also the Make:it motor driver board comes pre-programmed and you cannot upload any programs to this board. The programming at https://github.com/RadioShackCorp/2770168-MakeItRobotics-Starter-Kit is for an Arduino as well.
If you wan to go commando and go outside the box, http://www.joestechblog.com/category/robots/ has explained how the Arduino works with the motor control and sensors. With that he implies the Raspberry Pi could be used instead of the Arduino.
The simple answer is yes you can but with a couple of tasks before you will get it working
1. The Arduino talks to the board using software serial on pins 2 and 3 and has level shifter circuit to adapt to 5V (The Dragon chip is 3V3 as is the PI), this level shifter will need to be bypassed to make it all work at 3V3. (A simple task with a soldering iron)
2. You will need to study the arduino code to see the serial commands and responses used to talk to the board and re-code in python, C, C++ or whatever your programing language of choice is. There are a few LED outputs that can be connected to GPIO of the PI
You won't be able to monitor the batter voltage as the PI has no ADC (You could add a separate one.
The wiring will have to be via jumpers as the motor shield will not sit on the PI
