a global field is available from anywhere as soon as the Set field/set field by name script step completes or as soon as a calculation fires.
Just run your process with the script debugger data viewer open and you will see exactly when your global has changed.
And be aware of single user vs hosted solution uses of global fields.
If user A modifies the value of a global field, the change is not visible to User B and vice versa. For both users, any changes to the global do not persist (as would be the case in a single user (not hosted) solution.) The field's value will revert to the value in the field at the time it was uploaded to the server when the user closes the file.