Okay, so I may have misinterpreted everything I've read online so far about obtaining Rotom's Pokedex entry. But here it goes, as per my understanding:
In order for Rotom to appear in Eterna Mansion (or whatever), you must first have the National Dex. However, in order to obtain the National Dex, you must first have seen all 150 Pokemon.
The question, then, is where the hell do you see Rotom prior to being able to catch it in the Mansion?
Thank you for your answers, or, if I have misunderstood something, thank you for your correction.