Hey there!
In the case of multi-way speakers, so long as you have a low and high pass filter the impedances are not in parallel. However, if you only have a high pass filter and the 12" woofer is full range then the impedance above the cap cut off F will be in parallel, though the woofer also will have inductance that rises and may make this better than it would be otherwise.
Consider at least a single inductor on the woofer to help things along.
I often find it useful to use XSim crossover simulator to answer questions like this one when in doubt. It's free and easy to use.