I think the image you are basing your effect off of is using a "Volume" shader. This approach may be a bit easier. You have the right idea with the "Transparent" shader, but we are going to utilize the different render layers.
First, make two cubes, and scale the second one to the size you want the border to be. Add an "Emission" material to the Outline cube, and set the color to what you want. Then, move that cube to layer two, by pressing M and selecting the second box. In the bar at the bottom of the screen, you should see the same set of boxes. Hold shift, and click both the first and second box, so you are able to view layer 1 and 2 simultaneously. Now, navigate to the "Render Layers" panel. Name the current one "Base Cube," and check the first box under "Layer" and the second box under "Exclude". It should look like this:
Now, make a second Render Layer by clicking the plus icon. Name it "Outline," and check the second box under "Layer" and the first box under "Exclude." This new setup should look like this:
Next, under "Passes," check the "Object Index" box. Select the Outline, go to the "Object" panel, and set the "Pass Index" to 1. Do the same thing to the Base Cube, but set the "Pass Index" to 2. Now what we have are two cubes on two separate layers, so we will be able to lay the Base Cube over the Outline.
To do this, select the "Node Editor" menu, and select "Compositor." Check the "Use Nodes" box, and duplicate the "Render Layer" node using Shift+D. In the new "Render Layer" node, select "Outline" as the layer. Add an "ID Mask" and connect the Base Cube node's IndexOB output to the ID value input of the ID Mask node. Set the "Index" to 1, and add a new Mix node. Connect the Outline to the first image input, the Base Cube to the second image input, and the Base Cube ID Mask to the FAC input. What this does is add the Base Cube on top of the Outline wherever the Base Cube is. Finally, connect this "Mix" node to the composite image input. The nodes should be laid out like this in the end:
Time to Render!!! Select "Image > Save As Image" to save the outcome. This is the final result:
I hope this is the effect you are looking for. This is a versatile method for a number of things, and it should work fine with planes as well. Let me know if you have any questions. Happy Blendering!