Calculating a cloud cover index based on comparison of horizontal and tilted irradiance from pyranometers
Not being an expert in the subject, I agree with your hypothesis. But, I think that what you are measuring with the difference in the readings is the anisotropy of the illumination. In very cloudy skies, the amount of light from all directions in the sky is the same (that's why you can't tell where is the Sun). In a extreme case, like the condition refereed as whiteout (dense fog over snow) a pyranometer on any direction would measure the same value.

However, I don't think that can be used to calculate cloud cover in the common sense, as the anisotropy will be very high even if there is a small gap in the clouds that let the Sun light through, so your conversion into cloud cover would only work when the cloud cover is homogeneous, and would fail when it is patchy.

I would think that you have better chances to estimate clod cover if you have one pyranometer shielded from direct sunlight , so you can measure how much energy is coming from the sky. However, you would only know the cloud cover in that area, and still with many posible source of error.

Measuring cloud cover is a difficult problem. Naked‐eye observation of sky cloud cover has widely resisted automation. Some successful approaches use analysis of images like in Whole sky cameras or more sophisticated whole sky imagers.

However, there are methods developed to estimate cloud cover based on standard AWS data. Like APCADA, that uses longwave downward radiation, temperature, and relative humidity measurements. It is described in the paper "Automatic cloud amount detection by surface longwave downward radiation measurements", that reports that:


  APCADA estimates. Results show that about 86% of all cases agree
  within ±1‐octa cloud amount difference for sites with moderate
  climate, 82% for sites with arctic climate, and 78% for the site with
  tropical climate.


I would think that for the direction technology have taken, the most affordable options will go in the direction of having a camera taking pictures of the sky (in infrared if you can), and having and algorithm to analyze it and evaluate cloud cover. I found this paper that talks about that. It looks like the Red/Blue ratio is a good indicator to classify an image pixel as cloud or cloudless.