Sorry, this isn’t supported. VisualGDB projects refer to toolchains by unique IDs that are automatically resolved by VisualGDB when you open the project.
The path (neither relative nor absolute) is never hardcoded in the project itself. This allows opening the same project on multiple machines with different toolchain installation directories without modifying anything.
If you want to avoid installing the toolchain on each machine manually, you can simply create a .reg file that will register the toolchain location from your repository on each machine (see HKEY_CURRENT_USER\Software\Sysprogs\GNUToolchains) or rely on the VisualGDB Team Settings mechanism to deploy the toolchain automatically.