Well it wouldn't be free software, because the requirement to publish source code publicly is at odds with the free software definition; the freedom to do something is not an obligation to do it. Copyleft simply means that if you choose to distribute the software, that you must do so under the terms you received it.
https://www.gnu.org/licenses/license-list.html#Watcom
But, suppose the free software definition was written with this requirement in mind - as other commenters said it would be untenable, and potentially hazardous if you are using the software in a hostile environment.