This question really boils down to a more general one:
What degree of photometric precision can be achieved by a smartphone camera?
To put this question in context, let me give a brief explanation of what is fundamentally different about a scientific image sensor versus a consumer grade sensor.
As you would expect, a scientific CCD will usually have much higher quality than a consumer grade CCD. In this context, "quality" is quantified by dozens of characteristics of the CCD, such as the uniformity of the sensitivity of each pixel, dark current, defective pixel count, photoelectron well depth, electron lag, spectral response, bleed and saturation, etc. The superior performance of a scientific CCD is, of course, helpful in making a good measurement; but the really critical distinction of a scientific CCD is that each and every property of the CCD will be measured and tested before the CCD is ever put into use. In fact, when purchasing a scientific CCD one receives many pages of documentation detailing each characteristic of the sensor, and the testing methods used to measure those characteristics.
This knowledge of the behavior of the sensor is critical. It allows us to take the raw image data produced by the CCD, and make a very precise estimate of the light that we are actually interested in measuring. Even more importantly, it lets us quantify how precise this estimate is. As a general rule in science, a result is worthless if you cannot state how much confidence you have in it.
So what does this mean for making a measurement with a smartphone camera? It means the quality of your measurement will depend strongly on how much effort you put in to measuring the characteristics of the sensor. It also depends on what sort of measurement you want.
For example, if all you want to do is determine whether there is more light in one image than in another image, you could do a pretty good job just by looking at the average pixel values and comparing them. This is basically what is described in the article linked in the question. In this case you're using the same sensor in both cases, so regardless of the characteristics of the sensor, you can be pretty confident that a brighter image will result from a brighter sky.
As you try to make better measurements, you begin to require better knowledge of the sensor. What if you want to measure exactly how much brighter one scene is than another? You would need to know about the background level measured by your sensor, so you would need a dark frame (an image captured while no light is reaching the sensor); you would need to know if the value measured by each pixel is a linear function of the amount of light hitting the pixel, so you would need to expose the sensor to a series of illumination sources of known intensity and compare the measured value with the known illumination; you would need to know how likely it is that the observed change in image brightness is simply due to noise, so you would need to quantify the read noise, dark noise, and possibly photon noise. The list can very quickly become very long!
The short answer is that you probably could measure light pollution with a smartphone camera, but realistically it would be a very rough measurement. At the very least it would require you to be able to control the exposure time and gain (often called the "ISO speed") of the camera. In my experience, smartphones usually change these settings automatically, so you would need to write a special app to collect your images.