Can this C program , that uses purely an unlinked C stdlib and is compiled for Linux, run on Windows?

The question is a bit specific, so assume the following:

1. The program’s C source code does not explicitly use platform-specific functions (it does not explicitly use system calls, for example).
2. To interact with the OS, the source code uses the C stdlib.
3. The stdlib is not linked at compile time.
4. The program was compiled for Linux on a machine running Linux, then moved to another machine running Windows.
5. Before executing the program on Windows, the Linux executable is (somehow) converted to a format compatible with Windows.
6. Both machines have the same hardware.
7. Both machines have a implementation of the C stdlib.

Now for the question(s):

1. Given all the assumptions above, can the program execute on Windows? If not, why?
2. If there’s an assumption that is incorrect, why is that?