Speaker school is IN SESSION
2-way coax's in the doors may change the sound of the upper tweeters because....
1) Amps don't push power into the speakers - speakers draw power from the amp based on their impedance (ohm) rating. A speaker with a 2 ohm impedance will draw twice as much power from an amp as a speaker with a 4 ohm rating. This concept is critical to understanding sound systems. Learn it, love it, live it.
2) A 2-way coax speaker will generally have a lower impedance than a single speaker, beacuse there are two speakers in the circuit sucking up the power (rather than one).
3) All speakers in the circuit are affected similarly, depending on how they are wired (i.e., in series vs. in parallel - but don't worry about that for the purpose of this conversation).
So, let's say you have two 4-ohm speakers wired in parallel (one in the door and one in the dash) and you replace the one in the door with a 2-way coax with a TOTAL impedence of 2 ohms. In this configuration, the new coaxes will suck up a larger proportion of the power than the 4 ohm in the dash, and so you will actually reduce the amount of power running to the one in the dash, making it less loud. (Hotsauce, I don't have the time to reorient myself with the formulas and to do the math, but I am pretty sure the new setup will lower the power to the original dash tweeters.)
That said, the tweeter in a coax doesn't really have 4 ohm impedence rating, so the simplistic math suggesting that the 2-way coax has a total 2 ohm impedence is inaccurate. The true rating of the 2-way coax is probably closer to 3.2 ohms, which means that the power being drawn by the original 4 ohm speaker in the dash will be reduced only in slightly, so there will be barely any difference in how it sounds.
Once you throw passive crossovers into the 2-way speaker circuit, it gets a whole order of magnitude more complicated, but that's another topic altogether. I'll just add that MB Quart's crossovers used to be notorious for their inefficiency, making the speakers quiter at a given power level than other brands, so be careful of that when choosing speakers, and NEVER MIX. :-)
EVERYTHING is ALWAYS more complicated.