I know many people who do this. There are a couple of variants. The starting point in autumn is a national brood box with the brood under a queen excluder under the last shallow super they fill (ivy or sugar syrup say). Before the weather or season changes you remove the queen excluder to avoid the cluster moving away from the queen.
One variant is to leave the nearly full super on top. Then in late winter or early spring you hope to find it empty and the queen and brood still below when you can remove the shallow or put the excluder back. Leave it too late and there's brood in the super. Plus over winter the queen and brood are exposed through the OMF. So a variant is to move the nearly full shallow super under the brood. Stores will be used or moved as needed when the weather permits, the queen is less likely to lay in frames in the lower position and the brood gets less draught from the OMF. If you're dribbling oxalic in late December it's also more likely to be on the cluster just under the crown board. In late winter/early spring, the shallow box should be nearly empty and can be removed or it can go back over the brood box and queen excluder if there is early blackthorn coming in.
Yes, it probably is more moving stores and work for the bees, but on mild days they are active anyway. It's more work for the beekeeper moving boxes and monitoring. It's also probably more vulnerable to mice and very late wasp robbing. Timing, as ever, is dependent on weather; as it was to that point and as forecast. You're looking for all the stores needed being in (ivy finishing) but they're still active. Middle of October maybe when temperatures should be mid teens most days. It probably works better in the South with mild spells. I don't recall any entire week this past winter when I didn't see bees flying at least one day. Insulation slabs over the boxes probably gives a greater margin too. In a longer, colder winter you might be safer with them rising into the stores. In long cold spells the cluster could be high and isolated. Even with stores below, adding fondant above might be a useful precaution.
I tried a couple of side by side trials a couple of winters ago with brood box plus super of stores. Stores over or below didn't make a lot of difference. Some do try to reduce to one National brood box per colony over winter and they do fine. I'm happier with the insurance of stores that pass the winter unused. 14x12 is one way out of it, but for Demarees etc I like the versatility of standard deep National brood boxes. Placing that shallow of winter stores over or below will probably depend more on whether I see a weather window than any hard rules.
