Does Windows Movie Maker produce mp4 files?

No. Windows Movie Maker does not produce .mp4 formats. That file name extension (format) is not compatible with the program either.

These are the video formats compatible with Windows Movie Maker:

.asf, .avi, .dvr-ms, .m1v, .mp2, .mp2v, .mpe, .mpeg, .mpg, .mpv2, .wm, .wmv