You can change that by modifying the code in gidmapper.cpp and compiling Tiled. This will also affect the TMX files, which work with the same kind of global tile IDs. It could also affect code using the GidMapper since it assumes global tile IDs are unsigned, which can’t represent -1. And it would mess with the flags used to store tile flipping. Finally, you’d of course end up with a Tiled that is incompatible with everybody else’s version of Tiled, unless you implemented this as an option.
Probably subtracting 1 in your own code would be a whole lot easier?