If they were in the east, I think there would actually be a really good chance, but fantankerous does have a [exaggerated] point.
Minnesota could make huge strides next year and be a .500 team or close to it, but a .500 team in the West, might actually still pick around #12. Right now, for example, OKC is a .500 team and they are slotted to pick 13th.
Minnesota will need help in the form of one or more Western powers crumbling. This isn't outside the realm of possibility. Whether by major injury or free agency, if Memphis lost Marc Gasol, Portland lost Lamarcus Aldridge, Dallas lost Dirk, Houston lost Harden, or NO lost Davis, that would make a little room for Minnesota to climb out of the West's bottom 5.
San Antonio is awesome, but so very old. We've been waiting for them to slide forever. If Kawhi were to walk and Manu and Duncan were to finally age, they could fall into a rebuilding year soon (doesn't this have to happen some day?)
Stuff like this does happen on the regular. The Pacers abruptly vanished from contention going into this season. OKC nearly vanished, as well. Last year, the Lakers and the Knicks vanished.