No. With the standard setup the AMP if you can call it that feeds the rears speakers, and the head unit does the front speakers. With the Bose setup the AMP feeds all the speakers, so you would have to run the front speaker wires from the brown connector to the rear, and you would also need to run 2 wires for front left/right audio out to the AMP. Your also going to have to cut off the plug going into the current amp and and fit a new connect compatible with the Bose AMP.
You should also replace the speakers as the Bose speakers are 2ohm, and the standard speakers are 4ohm, they would work with the 4ohm speakers but it's best if you have the correct stup.