For a smooth steel that would be mostly correct. The edges really don't roll that often in my experience. They get dull, the smooth steel refines the edge through plastic deformation. Once they get that treatment a handful of times they just become drawn out and need something to remove some steel. It helps for the edge to have a bunch of grind path texture to it, so the high points have somewhere to smear. When they no longer have anywhere to smear to, it get mushed out along the edge.
A grooved steel does removes metal, works exactly like a fine file. If you use one on a smoothed out edge bevel you will see a new grind pattern forming - removing material and cutting a new edge. It has trouble removing the burr cleanly, but a regular file does as well. It can, just takes a bit of finagling. For a heavy used knife in a kitchen environment, it really doesn't matter if a bit of burr is left.
On the upside, these tools are not prone to bacterial issues and very handy to keep around. I used to use grooved and smooth steels in tandem to keep up on my kitchen knives for years. Also used them on my grass hook and corn knife.