Not really, since milk contains water the max temperature you can reach is 100 degrees (given it has a path to atmospheric pressure). So the bottom can only burn if all the water boils off.
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I gave it some thought, and a possible explanation is that water evaporates from the bottom of the pot, it leaves some waterless milk there, and that burns.
But this assumes that the inside of the pot can be hotter than 100°C, I wonder if that's true, or milk keeps it ~100°C (water is very good at transferring heat after all).