The green part of the scouring sponge thingy is basically Scotch Brite. This is a pretty agressive abrasive.
Wikipedia:
"The structure of Scotch-Brite pads is created by a sparse unwoven polymer such as cellulose, nylon or spun polypropylene fiber. Products use several variations of hardening and abrasive materials, such as aluminum oxide (alumina), titanium dioxide and resins.[1] Although the base polymers may be considered benignly soft, the composition with other materials greatly enhances their abrasive powers; to the extent that a heavy-duty Scotch-Brite pad (which contains both aluminum oxide and titanium dioxide) will scratch glass."
In my experience it is a more aggressive abrasive than steel wool. As with steel wool, make sure you do not get little bits left behind that find their way into the gun.
I doubt that the little bit of brass removed will measurably thin your brass, if you only polish it until it is shiny. I have often wiped my cases clean with a scouring pad after washing in my Citric Acid and Sunlight mix. This is done wet, so any residues are hopefully washed off, and the water seems to soften the pads a bit. I did not notice any scratch marks afterwards. Cases were turned by hand only. This was done in stead of dry tumbling, when I was in a hurry to get the cases loadable.
I do think that a moderate tarnish (oxidation) on the cases acts as a lube. On handgun cartridge with Tungsten Carbide sizer die, the un-lubed tarnished cases generally have less resistance than shiny clean ones. I guess the same applies in a chamber, but that's just my guess.
Lube in a chamber at normal to max working pressure is definitely not recommended. Locking lug set-back or shear may be problem on AR's, but I have also seen it happen on a Brno ZKK602 that was converted to 460 Weatherby. This is an extreme example. Normal medium caliber rifles will likely not suffer from this condition, even with some abuse.
Interestingly, under certain conditions lubed cases can actually extend case life. If you full length resize every time, the case will stretch quite a bit until it cracks or separates. If it is lubed, it will move back against the breech face without stretching. I would not recommend this, but it may serve the purpose of case forming with a mild load.
Anything can be over-done to the point where it can cause damage. Do it within reason, and it will be beneficial.