Any such prediction would be bound by the least precise constant involved in the calculation. This experiment is truly pushing the boundaries of distance measurement (to the tens of femtometers) so I doubt the rest of our measurements of universal constants are anywhere near precise enough to pull it off. If we could measure all of those constants as precisely as, say, LIGO can measure optical interference spread over many kilometers then it would be possible, but if we could do that we'd probably have already measured the proton's size to within femtometers.