"Would Mulder and Scully solve [insert mystery from a non X-Files piece of media here]" is a deceptively complex question because there are two different answers depending on which version of the show our hypothetical episode is part of.
In the one version, Mulder and Scully wildly misunderstand the nature of the problem in diametrically opposite ways, and eventually succeed in removing the immediate threat in spite of having no idea what's going on, but do so in a way that traumatises everyone involved and ultimately reinforces the status quo, because law enforcement agencies are institutionally incapable of solving real problems even when their individual agents act with the best of intentions.
In the other version, Mulder pulls the correct solution out of his ass in the first five minutes, but can't prove it because the evidence keeps getting Phineas and Ferbed the moment before Scully walks into the room, and the problem is fixed forever by shooting a sewer man with a gun.
The trouble, of course, is that these are both describing the same show.
the best part of each x-files episode is waiting for the end to see who's gonna do the sign off report cause when it's scully it's usually something like "once again, despite my partner's opinion to the contrary, i cannot confidently say that there is any scientific basis to the theory that alien ghost blood was responsible for the disappearance of the crack in the liberty bell" meanwhile if it's mulder we get gems like "are we alone in the universe? what does it truly mean to be alone? did bigfoot fuck the speaker of the house? as always i am left with more questions than answers and don't know who to trust and i think scully changed her shampoo and..."
one of my favorite things about xfiles episodes where the killer is a human with supernatural powers of some sort is that they're always like, "lol, it's not like anyone is ever gonna catch me. who would ever believe that the horrible accident in my backstory made it so that i can now control dung beetles with my mind and make them eat the brains of my enemies on my command" or whatever, and then ol' spooky Rolls Up and just goes, "i know about the beetle army, john, so why don't you just confess?"