Good question. I was worried about this too until I saw how the stock tweeter was wired in-- it had a fixed capacitor wired to it in parallel, with the woofer in series. That capacitor basically functions as the "crossover" in the system, letting only high frequencies in the tweeter and low in the woofer. Once you remove the stock tweeter (and therefore the stock "crossover"), you'll remove any of these filtering effects and should get the full-range signal to your new crossovers. This is barring any filtering that is done at the stock head unit, which may or may not be happening, but there's nothing you can really do about that I suppose.
2012 SE Sport 5MT 203A, Tuxedo Black