If you are going up a steep hill, it can be helpful, as well as going down a steep hill, but it would be best in the long run if you went into D3 prior to the trans. shifting up into 4th, so you aren't forcing it to downshift. Doing it preemptively in those situations is fine.

I used to occasionally downshift into 3rd while slowing down when I drove an auto, several different cars, but not all the time. In theory it can save a little gas and allow a little less use of the brakes, but the at the very least you are wearing out the trans. fluid faster, if not the clutch pack material, bearings, etc.
Pretty much the only Hondas where leaving it in D3 might improve the responsiveness, at least on paper, is the ones with the older style sportshift, where it's labeled S3. In that setting you can push a button on the shifter to choose between S3 (allows 1-3) or S4 (allows 1-4) and it holds lower gears for longer, so that in theory you are more likely to be in the right gear during spirited driving. It did work as far as holding lower gears, but unless you are in a lot of stop and go driving, or where you have to speed up and slow down quite a bit, you'd still get better mileage by leaving it in D4 - and it would still function the same at WOT, same shift points, etc. (pretty much pointless)