Built in sub crossover

The crossover circuit will definitely have an impact on the sound quality. Whether or not that impact will be audible (or bad) really depends on the other gear.

Are you contemplating a high pass connection to accommodate a pair of small speakers?

As far as I can tell the NHT B12d and SW12 are not equipped with low level (RCA) outputs or a high pass function. Both have fixed crossover selectors and low pass knobs.
Judging from a poor photo of the SW12 rear panel it seems to have a high level (Speaker) spring clip input only connections.

I can't find a manual or rear photo for the more expensive CS12.

While NHT produces economical products their functionality is usually better than acceptable.

I've ran my pre amplified front ends through a number of Velodyne and one JL Audio F Series subwoofer with little to no affect on the presentation yet I choose to run the main speakers full range.    

   

Some dyn floor standers and svs 12" subs

I run my system through my JL audio’s Built in E112 crossovers and I can’t hear a difference. The subs are the cheapest part of my system. 

Like all things it will come down down to implementation.