Like
@CX5_Driver said, sound deaden the doors. To give more insight into why replacing the speakers with the Bose amp may cause problems, it's primarily two reasons, IMO:
1.) Speakers with odd impedances. Speakers are generally around 3.2-3.9 ohms. Woofers are like... 2.1 ohms according to a wiring sheet I have. The subwoofer is 1.9? Ish? Something like that.
2.) Bose amp does NOT push out a lot of power. An installer in the Pacific Northwest believes it to be about 20 something watts for the speakers and about 40-50 watts to the woofers and sub (lower impedance).
Sound dampening the doors will reduce a LOT of the muddy sounds from the front woofers bringing out the tweeters and center channel. You may end up liking the system. Personally, I do not think that replacing the speakers are necessary for the MAJORITY of people. A good sounding car does not require aftermarket speakers or high end ones. Most of the good sound comes from DSP work, to which, Bose actually does within the amplifier. Time alignment being the major one. I believe there may be some crossover work as well.
Sound dampen first to see if you like what the standard system does. I ended up being happy with the way the tweeters/center channel sound. Much clearer, as the muddy woofers were reduced as well as the door vibrations. Really helped. I'll be installing a DSP/Amp using the factory Bose amp as an upmixer (basically) to retain Bose's time alignment and the 5.1 effect. I feel a little bit more power and the ability to EQ each speaker is going to make me happy with the system. By standard, the tweeters are neutral sounding (which is my preference) and not tinny or bright.