would using the woofer with the mid range cone, or possably the tweeter capture a more natural sound of the bass drum
"Natural" isnt the word I'd use for this kind of mic'ing in any regard. But there are plenty of variables that change the way a speaker acts as a kick mic.
A higher wattage speaker will have a larger, stronger magnet. Which in turn means it takes more force to actuate the diaphragm. Which would limit the dynamic possibilities of it.
As there's no circuitry to shape the sound of the diaphragm (speaker) as there is in a microphone, the frequency range is determined by the size. Large speaker can handle larger waves (which = lower frequencies).
Generally speaking the whole speaker as mic thing is designed to compliment another mic. To add a low end counterpart to an already full range (or at least mid-high) range track. Its not really expected to work well on its own.
- would using a tweeter as a microphone even work?
Any speaker can be a microphone. From a 1" tweeter to an 18" woofer. I have designs somewhere for a kick drum mic made from a 2" TV speaker as a matter of fact