At one point Odin came with win32k.sys (renamed to xx32.sys IIRC), which amongst other things, implemented what you're talking about. Click a Win32 binary and it ran. This even allowed the browser to launch malware just like real Windows, which is why it was depreciated and now I believe dropped.
There was also pe2lx.exe, renamed later to xx2lx.exe which will convert a PE (Win32) file to LX (OS/2) file, exes and dlls IIRC. That was a better route.
There are old versions of Odin around that have these programs. In some ways they were better for running programs too. Development of Odin for quite a while has more concentrated on stuff like compiling Windows code to run natively. Java, the Flash Wrapper, Acrobat etc.