You could.
First, you need to replace the drivers on the driveshaft to accommodate the extra lug height in the bulk head. Using tooth count and pitch (2.52) to find circumference, you can find the diameter by dividing by pi. Then measure the clearance between various diameters and the bulkhead and determine the tooth count needed, and purchase them if available. Remember to leave some space above the lugs to ensure no rubbing and proper snow evacuation.
Now that you changed drivers, you have lowered the effective gear ratio. You will need to regear the chaincase to get some speed back, and put enough load on the engine. The final ratio still needs to be lower than stock to have enough torque to drive the track.
Next, you may need to reposition the suspension to get enough tunnel clearance to clear those lugs. Make sure to keep the same geometry, or you will have binding. ie, move the rear down 1" move the front down 1" ect.
Keep in mind that the 600's power and ability to drive a big track. To keep the torque at a reasonable level you will need to lose top end considerably, but it will have better throttle response and get up and go in deep snow and technical riding when done right.