Passive radiators, ext crossovers & subwoofers

Do crossovers work equally well with speakers which include passive radiators?

This may be a silly question, but I asked it anyway. I don't know much about passive radiators. I have a pair of Polk Audio Monitor 7 speakers and I'm considering adding a subwoofer to help out in the lower frequencies by applying a crossover. If I set the crossover at 60, will the speakers continue to create sound at frequencies below 60? Or does the passive radiator create the sound only at the frequency delivered to the speaker?
All speakers will continue to produce sound (though rolled off) below the frequency you select on your x-over unit - at the rate specified by the x-over function. Whether a passive radiator or active driver, the input signal is attenuated by the x-over at the specified rate. If the speaker is dead-on accurate in-room (none are), you'll have the precise roll-off you selected.

In practice, the room is mucking up everything at these frequencies. I use a Velodyne SMS-1 sub controller to view (and corrrect for) room effects. I like this approach a lot and highly recommend it. Note: I also use an NHT x-1 to roll off my main speakers because I like it better than the internal hi-cut function in the SMS-1.

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".
In my understanding the passive radiator acts in the same way as a port, to relieve internal pressure inside the enclosure and to simulate a larger enclosure. This is probably a gross oversimplification but it is not driven at all by the amp and has nothing to do with what you are doing. If you choose 60 Hz as a crossover point that means that the speaker BEGINS to attenuate at that frequency and the rate of attenuation depends on the slope of the crossover [6 db, 12db etc.] So you will be getting response below the chosen crossover point, how much depends on your particular system.
Keep in mind the higher the frequency you roll off the low end the less effective the passive radiator becomes. The passive radiator will be out of phase with any sub you use so from my own experience you are better to blend a sub with the polks using the above mentioned velodyne or other bass management system and run the polks full range
To clarify,

The passive radiator (if properly designed) is designed to produce output mirroring the electrical input at the speaker's terminal - exactly like an active driver. If you attenuate any frequency at the input, a properly designed speaker - passive or active - will attenuate the output accordingly.

Good Luck.