The crossover on the tweeters atleast on my interga is jsut a cap and its connected to the tweeter. Im pretty sure the tweeter itself actually recieves a full signal from the radio but uses a capacitor to filter the lows so that it doesn't blow up. Someone correct me if Im wrong.

You can just run the wires to the coaxil in the door and disconnect the tweeter and the new speaker will play full range.

You can do components and they to tend to be of higher quaility than the coaxils (ones with tweeter built in). If you do go this route i would highly recomend an amp. It will really improve the sound. They really cannot be at their fullest potetial without one imo.