Fractional freezing: does it really work?

If I take a 500mL solution with ~12% ethanol, and freeze it for a few days, could the ethanol concentration increase to 20-25%, or even more? I've heard some of the alcohol would be frozen, but the net result would be a more concentrated alcohol solution (since some of the water would freeze). Is that true?

What about Methanol? If I prepare the ethanol solution with ONLY yeast and sucrose (no fruits whatsoever), would I still get Methanol as a byproduct? If so, can fractional freezing be potentially dangerous, since it can make the Methanol more concentrated?