There are different ways to use the global rackspace depending on one’s needs but not how you are describing it. If you are going to have instruments and effects in different rackspaces (that;s the normal way), then you may never even need the global rackspace.
For most keyboard players, the idea is to use the global rackspace for final effects processing. For example, instead of sending your plugin outputs to the audio output block in individual rackspaces, you might send your plugin outputs to the global rackspace where some final tweaking such as global reverb, global eq, global compression or limiting might be added. Control over routing to specific audio channels might be done there as well.
That’s how I use it myself.
Others might put an instrument or two in the global rackspace if it’s used on pretty much every song though IMO unless that instrument is sample based, it’s generally still more convenient to put it in each rackspace where it’s needed - remember also that rackspaces can be reused in multiple song parts.
Guitar players will often use it quite differently from keyboard players. For example, they might take the audio input of their guitar immediately into the global rackspace, possibly compress it, and then send it to different local rackspaces where each rackspace essentially represents a different set of effect pedals.
There’s not right or wrong way