Not sure if I'm understanding the question.
There's low pass and high pass components of a crossover. A sub, fed independently by interconnects, would only include the low pass filter, in which case the main speakers still receive full bandwidth. A separate active crossover, such as a NHT X2, includes both low pass and high pass filters. There are many ways to integrate a sub, including speaker level.
A passive radiator plays no part in your plans, except that it can be "tuned" or weighted (usually with blu-tack) to adjust the "Q".
There's low pass and high pass components of a crossover. A sub, fed independently by interconnects, would only include the low pass filter, in which case the main speakers still receive full bandwidth. A separate active crossover, such as a NHT X2, includes both low pass and high pass filters. There are many ways to integrate a sub, including speaker level.
A passive radiator plays no part in your plans, except that it can be "tuned" or weighted (usually with blu-tack) to adjust the "Q".