Well chart plotting is generally not going to be a single plot half way across the earth. Obviously there are obstacles and likely stops you want to make in between. Chart plotters will not show anything useful zoomed out to show the whole Pacific and Indian Oceans, if they will even zoom out that much. Great Circle routing is generally done for aviation navigation as they are not worried about most islands getting in the way, and then you have to take jet stream into consideration. But for nautical navigation it is more of a vague notion, not a single plot. You will veer due to currents, and prevailing winds. You rarely worry about the "shortest distance" especially in a sailboat. A globe is good at getting an idea of what you might want to see along the way, but won't give much else useful.
While you can use a chart plotter to see your progress on such a trip, they are more useful in more confined waters, and making sure you are on the general path to get where you want. You can zoom in to see reefs and rocks when you are near land.
Other than that I am not sure what you are looking to accomplish. Yes you can draw a line on a globe to give you general distances. There are web sites to help with the calculations (Marine Great Circle Navigation Calculator
is one) as they can get pretty complicated when trying to get a distance along a path on a sphere. (You should see the math wars that go on on geodesic dome forums!) But those are not anything more than general guides and will not even give an accurate path you will actual be sailing.
Oh and by the way those cheap (dollar store) beach ball globes are really not recommended for navigation! :-) And really not good to use pins on them either! ;-) Actually I had one that was funny it had wrong continents, let alone countries.
Actually giving it some more thought, using a chart plotter, or even a large scale chart and drawing a line from HI to the tip of Cape Horn is kind of like me grabbing a map of the mainland and using a ruler to draw a line from New York City to San Francisco, saying that is how I am going to drive from one city to another.