It would, but those tip cleaners will restore a *lot* of tips.
I tried the little cans of tip cleaner/tinner when I had a Radio Shack iron with the pure copper tips with the micro-thin nickel plating. Wrong thing for that job. Those tips just die, and once the plating is gone, you might as well just file them. If you're counting on some black magic where this stuff restores the actual plating, it does not. It works by removing material, and the "tinning balls" in there might as well be regular solder. Don't get me wrong, it's good in the fact that is gets into nooks and crannies, removing mostly just the oxides and not the good metal. Also there is advantage in solder holding ability if you leave the surface textured/micro-pitted, by using a chemical cleaner. But in average tip, there is plenty of iron there, and the "gentleness" is not needed, if you stay away from the thin chrome plating.
With proper temp controlled station, it is rare to ruin a tip at leaded solder temps. It's not that buying a new tip would be cheaper... just that a stone or sandpaper is a generally useful thing the rest of the time it's not needed for a soldering iron. It just depends on what iron you got and how you use it. I have tried to intentionally oxidize a bevel tip on my old velleman station. Trying to make a CF tip. I sanded the tip, tinned just the face, and left it at 450 for several hours. It still tinned like nothing happened. In hindsight, after reading this thread, I could have coated it with zinc chloride flux to induce surface "rust."
Update on the steel wool. My own firsthand experience now says, yes. It's too aggressive. It is wearing away at the edge of the chrome plating, already. At least on the Chinese T12 tips. (But boy does it clean crusted residue - it gets down to the chrome, removing that last layer of residue that brass wool leaves behind). I can tell the difference between the real hakkos and the Chinese knockoff. It's the level of machining/polish on the tips before the chrome plating is put on. The Chinese tips have profound grind marks and also voids/defects from the casting/MIM or however the iron part is made. I'm sure the real Hakko chrome plating won't break/flake as easy. It's just a matter of how much time and $$$ spent in the manufacturing process.
As an experiment, I filed away at the working end of the tip deep enough to remove the machine marks. No surprise to me, the copper is not exposed and the tip still works. I'm sure there is a lot more iron there. I have cut apart a few of them. If the iron was chocolate and the copper was caramel, it would look like the cross section of a Rolo. When you consider the prying/twisting forces you can put on these tips, you know there is considerable iron there for structural integrity as well as to protect the copper from dissolving. If it was just a thin electroplating, I would have bent some of my tips into pretzels, by now. Dropping the handpiece on the ground, point down on a CF15 tip, it would be bent at least 45 degrees at the base. Instead, this results in just a tiny curl at the edge of the tip.
The very existence of the deep machine marks in the Chinese tips is indicative of the thickness of the iron. These kinds of marks would not be left on copper. Copper would be cut and swaged, and any grinding/polishing would not likely be so rough. The machining is surely done after the tip is made, just before the final chrome plating. If there's enough iron there for the factory to grind on it with what looks like a 60 grit belt, there's enough for gentle sanding, galore.