dungeons and dragons: do players know when their attacks are connected?

Now, this is a rather strange question, perhaps. But depending on the narrative style of the game, "hitting your armor class" does not always mean that you physically hit your opponent with your weapon. Personally, I like to describe a "blow" as "you really had to strive not to be stabbed by that sword." In general, at least.

However, in this narrative style it raises a potentially interesting question, and a trick related to DM *. If an attacker does not really score a significant they hit until they really take down a monster, do they necessarily know when they are inflicting HP damage? It is quite common for players in combat to save time by throwing damage dice along with their hit dice. Could a DM require that of the players, take notes as needed and only inform the PCs when an attack really does something (like tearing down the target)?

*: As a DM, I must say that I don't think this is something I would do in many cases. Knowing the CA's stage of the target is a useful meta-knowledge for the player, which generally does not affect the narrative in any way (beyond "A 14 is not good enough to hit this guy, but a 16 is better use my Bardic's inspiration dies "). While being denied does not necessarily improve the experience, in fact, it would probably introduce frustration for some players ("Man, are we even hurting this guy?!").