Yes, if you consider DOS to be acceptable. Otherwise No. The exe would have to contain all the drivers for the hardware as well as the application. An OS is just a collection of EXE files. Many of them specialized.
Of course it won't run as the operating system, but you can easily setup the program to run at start up and then use system policy to disable normal Windows features like taskbar, access to control panel, etc... This type of thing is called kiosk mode often.