Perhaps, if there are some very specific compatibility issues that haven't been solved yet.
That said, MS-DOS 4 isn't even the most recent version, the last one was 6.22 to my knowledge, and IIRC a lot of games tended to require at least version 5 or 6.
2 things, the project exists and is called ReactOS. 2nd, the kernel in the versions of Windows anyone thinks about is the NT kernel which they will never release to be open source. The NT Kernel was built specifically so that they didn't have to use DOS to make Windows work.