Do I need a sub?

My main speakers have built in powered subs that will go down to 20 hz and I still have an additional separate servo power sub.and it adds fill and energy to the room. Requires a little work to integrate, but worth it.

Short answer, Yes.
Practical answer, Yes.
WAF answer, maybe.
Like millercarbon, I run a swarm, 2 10s and 1 12. I have a 15 in the garage, large, ugly and unused so far. I use one amp for all 3, utilizing a DBX 223XL crossover set at 40 hz. I plan to add another 12 or 10. The amp is a Denon POA 6600 mono block with 265 watts at 8 ohms.
Utility.
My goal was decent bass at low level listening, without needing to turn the subs up at low volume or turn the subs down at hi volume levels. All sub boxes are sealed or acoustic suspension as we used to say in the early 70’s. To save money, the boxes and speakers are sold/used for car stereo use. All of the above except the Denon cost less than my unused Velodyne 12 dedicated sub.

I use a Lyngdorf amp to run RoomPerfect room correction. It perfectly integrates the sub to the mains, 4th order LR filters at around 75Hz. Nice.

Short answer. Any system will benefit with use of sub(s). Biggest gains will come from using high pass filtering on main amp. Let sub amp do all the heavy lifting. This will benefit SQ all the way around, not just adding hertz on the bottom end.

Arc, Mr-m has it right. Every system benefits from subwoofers unless they are already built into the main speakers. Do not bother with a single small sub. You will not be happy. Two 6" drivers can go extremely loud if you remove 100 Hz down from them. You need at least two 12" or four 10" subs to get anywhere. Most subs now come with plate amps and cross overs in them. You absolutely need a crossover with a high pass filter for your main amp as you suggest. Unloading the main speakers is one of the major benefits of using a sub. You will clean up everything else those 6" drivers carry. For those of you who do not believe in Doppler distortion just have somebody drive by you at 30 mph leaning on the horn. The sound will go from a high pitch to a much lower pitch as the car passes you. Towards you and away from you just like a woofer pumping away changing every other note it carries. 
richtruss, the Lyngdorf is a crippled version of Radomir Bozevic's original design. The Trinnov is much better but still not up to Bozevic's design in some ways.