No; both the operating system and user programs on Linux Mint, and it's Ubuntu/Debian base, adhere to FHS (
https://en.wikipedia.org/wiki/Filesyste ... y_Standard). GoboLinux retains compatibility with FHS, mapping paths used by FHS compliant programs to respective areas of its own filesystem hierarchy. But, programs for Linux Mint are installed from Debian packages (with an APT package manager) and each package details where in the filesystem hierarchy each of its files should be installed. That part is not compatible with GoboLinux.
In short, you can run Linux Mint programs on GoboLinux (as long as you install from GoboLinux compatible packages). But you can't run the GoboLinux filesystem hierarchy on Linux Mint without replacing also the package manager, and that will mean you can't install Linux Mint programs...