Doesn't look like it.
It has no detail, so I have no clue what this is even for. As I said before, I went to EVERY auto parts store in town (NAPA, Carquest, Autozone, Advance, and Thirlby's) and NOBODY had the kit. If my Advance doesn't have it -- and doesn't even know that it exists -- then I'm pretty sure that yours isn't gonna have it either.
The W-1, while a solid carb, is REALLY OLD. Most car parts places don't have parts for anything older than 1960. I'm lucky, because my favorite FLAPS has data and parts for stuff back to 1946 on some things, but I'm unlucky in that they don't have any data for other items -- like the carburetor.
Check out the two vendors that I mentioned in my previous post. They have the right kit. I've linked right to the pages in their stores where the rebuild kits live, and you can buy them quickly and easily without any muss or fuss.