Mid range woofer crosssover cutoff question?

No, it wont damage them, but it will only affect sound quality.

If you look at typical Coax speaker, it's basically the same thing.

Regular cheap coax have a unfiltered mid-woofer and a Tweeter. The tweeter has a single capacitor as a simple 1st order High Pass Filter. Basically the mid-woofer is run full range, with no low pass filter.

On some better quality Coax speaker, a coil/inductor is use as a simple 1st order Low Pass Filter on the mid-woofer. High Quality Coax use more complex crossovers (2nd/3rd/4th order filters, zobel, etc..).

Note: Coils/inductors "block" higher frequencies and most speakers have coils, they "block" them because as the frequency gets higher, the coil's impedance(ohms) also gets higher. Higher impedance means less power and less sound, this is why it wont get damage and has a maximum recommended frequency response.

So, if you want you can just use a coil/inductor series with your mid(s), to cutoff the highs. To approximate what size coil you need, go here: http://www.the12volt.com/caraudio/cross4ohm.asp

(I say 'approximate' because choosing crossover component to get accurate results is fairly complex.)

Or you can go "Active".

Use electronic crossovers, buy an amp with band-pass capable crossovers, or buy a headunit with 3-way/bandpass capable crossovers.

REL makes, via a ways, between the main suitable sub-woofers - it is an business enterprise dedicated to that one product and is truly solid at it. i'd advise bypass with REL - I even have been employing REL sub-woofers for some years and would distinctly advise one.