"Why not use one of the thumbnail labels to display the {caption} variable"
Then I need to be on that image to know if it's captioned.
I'm hoping for something more obvious like a blue folder is partially done a red folder is finished.
Not at all. You can set up PM to show one to three rows of variables that is displayed under each of your thumbnails in the Contact Sheet so you can easily see if a file is captioned or not. This combined with a sort by Caption gives easy way to find it out even if you use a basic caption to all your files upon ingest as I do it. (I find it quite easy to discover an image captioned manually as my standard captions start with different parts (general information of the shoot) and those I manually caption get pepople names and descriptions of what is in the picture.
You can also use a sort by modification time as probably images you captioned were modified later than the rest of images you did not caption yet. This combined with the labels displayed under the file name mentioned above give you quickly what you want.
But you can also use tags, color codes or star ratings or even adding a keyword: captioned or done to see if a photo has been captioned or not. For those captioning on ingest any variable showing to have a caption would be a waste of resources as there is no image without this state. I don't have any uncaptioned images ingested. I caption images with a basic caption during ingest and later I manually edit it if needed.
On my part I tend to use no color for no edit or at least "needs some care" images. Those I finished cropping, captioning, keywording, etc get stars or color codes and I can filter them out not to appear among the others that still need some edit (or to display only those that are complete). Even my untouched images do have some kind of caption. At least event name, location, date, copyright. But I only add color classes to them if they are at a level of edit and the color tells me where they are in the process.
Actually it is totally up to your workflow to decide how to use any of the already existing marking techniques. There are tags for example that can be used to mark if you did caption an image or not. But it can be used a number of other ways as well it is up to you how you want to use it.