It is possible to use it as a agitator to work in the chemical product to reduce the time or heat needed for the product to work.
In that instance you could do just as well with a wool or terry bonnet, as it will not heat up the fibers as much as a brush. The fibers ina car are very heat sensitive.
Now if you wanted to aid your drying process after you cleaned the fiber, take a clean dry bonnet or wool padd an run it over the top of the fibers, switching bonnets when it becomes too wet.
This is commonly refered to as bonnet cleaning, In many cases i have used it in comercial buisness to keep the fiber from wicking caked in dirt up to the surface. Carpet and fiber dries top bottom up. It evaporates from the surface drawing the remaining moisture to the surface, in many cases bring the dirt and grime with it. It's rare for it to bring dirt from the backing, or pad. It's possible but you'd have to basically flood the car.
In reality even with the best combo of systems you can only clean about 70-80% of the fiber carpet surface, so you will have grime and soils left in the carpet. The key is to leave so little moisture that the carpet does not have time to migrate those soils to the surface.
To do this you should follow a very tight regimn of cleaning proceedures.
1) dry vac
2) dry vac again.
90-95% of the soils in the fiber are dry particulate dirt, best removed by dry vacuuming. if you add moisture to a poorly vacuumed fiber/carpet you have to work 10 times harder than needed with 10 times the amount of chemical and water than is needed. With 3-4 times the drying time. So dry vac very thoroughly. Use multiple attachments.
3)Pre condition stains and spots.
Why do this now? Because stain removers work best when applied to virgin stains, In many cases if not all that i can think of right now detergents will inhibit the stain removers if applied before the stain remover. So spot treat trouble areas first, Buy specific products for those areas. lightly rub them in and let them sit while you prepare you chemicals for the main area.
4) Pre treat the fiber/carpet with cleaner.
use a proper cleaning product. Read the dilution ratio's More product is not better or, lower dilution. These products work in conjunction with water, improperly mixing them will provide very poor results. Normal carpet cleaning agents are 32 parts water to 1 part solution. Once applied Brush in with your brush or PC if you feel the need. Despite what you think agitation will not improve your dirt removal. In many cases you'll keep the detergent from working by agitating too much. In some cases you will distort the fiber. (velvet it) The purpose of agitation is not to break dirt free, but to get your cleaning product to as much surface of the fiber as possible. So light agitation will suffice.
5) Extraction,
You can use a bonnet method i mentioned above, think Chem-dry the nationally owned chain.
You can extract with shop vac and 1/2 gallon pump sprayer of clean water or water 1ith 1/2 oz of vinager mixed itn
You can extract with LGCM or similar tool.
You can extract by buffing with a towel.
You can use a HW extractor.
The key is to get the fiber clean, then get it dry as possible, then get it set up for the shortest drying time as possible.
6) Drying.
There is little air movement in a car, So turn the fans on crack the windows, set up small portable blowers. The faster you get this dry the less soil wicking you will have. Adding significant air movement and ventalation will cut drying time in half if not by 3/4. Adding the bonnet buffing i mentioned befor can make even a HW extracted carpet dry with in 45-1 hour of finishing.