By manually impacting and cooling drill bit in water may one slowly drill concrete and bricks without impact function?
Impact drills are used in concrete and stone, with the appropriate drill bits, because they drill faster by causing micro fractures of the material surface and thus easier removal. The drill bits can get rather hot in the process.
It is still possible to drill holes in concrete with a regular plain rotary drill with the proper carbide tipped drill bits. It takes a lot longer to drill this way and the hole often ends up larger than intended because of the tendency of drill bit tip to wander around when pressure is applied it. The drill bit can indeed get hot but I've never actually seen the drill bit get so hot as to melt. Far more likely the end of the drill bit is going to wear away due to abrasion.
There would be nothing to stop you from repeatedly removing the drill bit from the in process hole drilling operation and cooling it with water when using either the impact driver or the regular electric drill. In fact you could even have a small stream of water running at the hole being drilled to help cool the bit.