Questions about integrating sub with monitors, power usage and driver age

When integrating a sub with speakers, does the sub reduce the load on the speaker drivers? In other words, say I have a pair of bookshelf speakers that can reach down to 60 Hz, and I combine it with a powered sub and set the low-pass cutover to 80 Hz, does it free up the bookshelf drivers by not having to reach down the extra 20 Hz? And does that then mean that more of the amp's power is dedicated to a narrower frequency range? If so, would this result in an audible improvement in SQ?

Second question, can anyone verify if the following is true?

"Unless the speaker is hardly ever used the life of a driver is typically 7 to 10 years if it's used regularly and turned up frequently. They can still make sound after that but the voice coils become worn and the response becomes mushy."

The only way to reduce the load on the main speakers is the use of a high pass filter. I doubt that ten year old speakers have worn voice coils!!
The low pass filter is when the sub(s) are being run from the preamp with rca cables.Your speakers would be running full range. To take a load off of the speakers you would use speaker wire from the amp to speakers and speakers to sub(s).
You would need something with a high pass filter. Some subs and integrated amps or preamps and AVRs have them. 
" To take a load off of the speakers you would use speaker wire from the amp to speakers and speakers to sub(s). "
That will not take the load off the speakers. Without a high pass filter the speakers will run full range!
I haven't used the bass section on my speaker system for years, they don't work right because of 1st and second order XOs, the timing just can't work..and they were the best in the business at the time. I use very little room treatment, too. I don't have too. Where you place separates really matters...

I cross at 300hz up with a passive crossover for the monitor section, 100-300hz  mid bass columns, (my Columns) with full blown DSP, active monitoring, on the fly change,  par/EQ and graphic/EQ, (everything). 20-100 hz. GRs servo subs. That system will last 25 years, then a refoam, good for another 25. I have ribbons that are 35 years old work perfect... Nothing to wear out. Unless you overdrive them, or use cheap amps, and tear up the drivers (Kid stuff). Outlast YOU, Ay?

Thanks for the responses. I actually do run my sub off my pre-amp/DAC. I have a JL Audio Fathom 110 (w/built-in amp) hooked up to a Mytek Brooklyn DAC+ with the balanced outputs on the DAC feeding the sub and RCA outputs feeding my amp. The way I understand it, the sub takes over bass duties at the LP frequency. I'm no sound engineer (obvious?) but it seems logical that the speakers would be doing less work by not having to reach down so far into the bass region, and that the watts coming from the amp are working more efficiently in a narrower frequency range, which then leads me to believe it would produce a slightly better SQ than if the power were spread out over a wider and lower frequency range. Is this not how it works?