David, I think you are correct in assuming that it matters. Technically, it absolutely does. Stepping through the grits gradually allows you to decrease the size of the scratches, which absolutely leads to a higher performing and long lasting blade. Skipping grits results in the polishing of a serrated edge.
I'm not sure if you are shopping for stones or not, in which case, I might want to change my answer. But my advice is to polish the backs of your tools using as many steps as you can/or as practical at the initial honing. Thereafter, for follow on honing, I only ever touch my backs to my finest stones- no reason to reflatten. Raise a burr on the bevel side and polish it off on the back with the least work as possible (to maintain the polish and flatness).
Now for bevel honing, my advice is to hone OFTEN and using the finest stones practical. If you can get away with honing on your finest stone for every hour of of work, I would do that, rather than hone less often and have to use coarser grits. Ask someone like Warren Mickley how frequently he grinds his tools and he may say "every 25 years or so". He's clearly doing something right since his Stanley #4 beats all comers at the hand plane events. I've adopted his suggestions and I find I am constantly using razor sharp tools and honing takes 2 minutes. But I do it every hour or so, sometimes more, sometimes less. Unless my edge fails, or I nick it, I use only washita and fine translucent arkansas. I do still grind more often than Warren does tho. Maybe every few months. Oh and I strop frequently too. Craft store suede, charged with the green chromium oxide crayon. The suede is glued to a piece of mdf.