How loud you listen and the amount of bass in the music you listen to will determine whether or not you should drive the speakers full range. My recommendation is to always use bass management with stand mount speakers (and the vast majority of floor standing speakers, too). The high pass filter built into the sub has distortion orders of magnitude less than the distortion produced by the woofers in the stand mount speakers. Woofer distortion can quickly exceed 20%.
Doing a sub setup "by ear" can easily lead to poor results. To really know what is going on in your room with your speaker system you need an SPL meter and a disc of bass test tones. You can download test tones from the Real Traps web site.
In order to utilize external bass management an integrated amp must have both preamp output jacks and main amp input jacks. The majority of integrated amps do not provide both.
Parasound seems to be one of the very few manufacturers that provide bass management for 2 channel systems. HK used to have a nice unit, but it I didn't see it at the Harman Kardon site today.
You might enjoy reading some of the white papers from Harman, specifically "Getting the Bass Right":