I definitely can, with the EXPORT command. The Windows, OSX and Linux executables you see have been produced like that.
In reality, they are just a common PICO-8 runtime executable (+ some shared library e.g. DLL depending on the platform) + a .dat file which contains the compressed Lua script + assets data.
So it’s just the .dat file that characterizes the game, while the pico8 runtime binary is just a common file for all games exported on a given platform, with a certain version of PICO-8.