No, it's not. Do read again. Do try it. Compare results. Repeat.
The second trick they employ is injecting noise in the input. They are essentially making a sigma delta on top of their a/d. But this again is nonsense... I wouldn't trust that. First of all your 'random' generator is not going to be random at all. It'll be based on a prbs polynomal.
You missed 2 points:
1. It is not just "a noise". If you superimpose 10Vpp noise over 250 mV signal - it wouldn't make any sense. You need artificially produced noise "with a ripple peak-to-peak value of a few LSB" (page 9).
2. It is not designed to replace 16-bit ADC with el-cheapo 8-bit. You are losing sampling rate at exponentional progression. For each additional 1 bit you have to double the number of measurements, so for getting additional 8 bit you will need 2^8 oversampling.
So far, you are just theorizing. Just give it a try and let us know of your results. If you still not satisfied - let's summon Atmel people here and question them a little bit Torquemada style.