Does Mickey Mouse exist in the DuckTales universe? (or even the general Duckverse).

It's a bit complicated, here. First problem, there are many different universes/continuties in Disney; second you want to know about the existance, not the appearance, which is a detail that the current accepted answer fails to aknowledge.

The easiest bit of knowledge is the fact that Mickey Mouse and Donald Duck, in the "main Disney continuity" (usually referred as Mouseverse) are close friends. Actually in the main continuity all of the Disney comic characters exist, and crossovers are not so infrequent.

Outside of the main continuity the pairing of at least Mickey and Donald is a very common event: they have shared comic adventures, been together in countless movies (which are often "canon" and referenced decades later), videogames, and so on. The same applies to a plethora of other characters, even if it's a little less common.

So, in general we can sum it up to: