Yes that is possible. Usually though the problems are in getting the correct amount of carbonation not in uniform carbonation.
Also with your theory it would not be possible to get an accurate reading form the first runnings as the amount of sugar in the mash is increasing until 100% conversion it met. The second runnings would encounter the same issue as you would be adding water to what is left of a wet sugar and grain mixture. Without boiling neither would be uniform enough to get an accurate reading. You certainly could not create mathematical model based on such inaccuracies, like a batch sparge calculator for instance
The cheeper refractometers like the atc ones are unreliable. I know this first hand due to being in the beverage repair business for over 10 years. I have found that the atago refractometers are durable and stay calibrated, they are a bit more money but worth it. Www.atago.net
What good is the refractometer if the gain is not linear? I would imagine that really throws off the FG calculations too. I wonder if that is why every model for determining FG is different: they all used their own variable refractometer.
Is there a solution? Maybe buy a better refractometer? Or is this a permanent flaw in the refraction through the prism? It seems odd that these tools have passed the test of time with wine, but they don’t work with a standard curve using sucrose.
Buy a good one. Avoid dropping it - as I have done more than once! I must say that I have only broken 1 hydrometer in 22 years, so I have that going for me, which is nice.
It does give a quick check of the gravity, so it is expedient.
Search ebay for “brix refractometer”. It’ll cost about $19 including shipping from Hong Kong. When it arrives, check the calibration. If you got a bum unit, buy another one. If that one’s no good, buy a third. You’ll still be ahead of what your LHBS would charge.
I don’t know how good it is, but my LHBS has a cyber Monday sale that has a refractometer for $25, regular $89! Pulled the trigger. Will zero and check the calibration.
+1 to this. If you can be patient, then watch homebrewfinds for when one goes on sale at a good price. I got this one on sale for $16 and I’m very happy with it: Amazon.com