He certainly does.
While on that topic, a quick disclaimer from me: I have not read any cosmere works outside of the Mistborn series. I have very little knowledge of all of the other stuff he has written, and no doubt this will impact the way I GM this RP.
I'm tangentially aware of stuff from the other books, that there are other shards beside Ruin, Preservation and Harmony, each with their own worlds and magic systems. I'm aware that there is some background crossover stuff going on between books, and that this will probably increase over time, but I'm fuzzy on all the details since I haven't read the other books.
So, yeah. If you're expecting other worlds to play into the plot of this game or for references to be made to Stormlight and others, you'll be disappointed on that front. I do plan to read the other books eventually, and expect to enjoy them greatly when I do, but for now this will be a solely Mistborn game. I hope everybody can be OK with that, and refrain from posting spoilers.