Well, searching for the terms "pokemon game maker studio", gives me at least one wip project on Steam, a youtube tutorial series, a Github project, and several people asking similar questions on other forums.
I think I can still do it in GMS. Though it'll take quite a bit of planning first before constructing a game.
So, I'd say, yeah, you probably can do it with game maker, though personally, I wouldn't stick with just drag & drop, I would make at least some of the project in Game Maker Language. (Is that what its called? I know it has a scripting language...)
I'm not so sure of the capabilities of GMS though, so I can't say much beyond this.