Does Sugar Cook Eggs?
It's not really chemistry¹, but simple physics:  you can have the same result with salt. (and an experiment you can easily replicate at home: salt is much cheaper than sugar).  

What happens is that the salt and the sugar and a whole lot of other things indeed absorb the water in the egg, which makes the proteins in the egg unfold, hook into one another and make these dehydrated eggs look just like cooked eggs where the heat does the same thing: unfold proteins.

Even if you add water again, these polymerized proteins will not re-absorb the water as they cannot unfold just like with a cooked egg: you can easily boil an egg, but it's hard to melt it again afterwards...  ;-)

So it's a common misconception as the cooked and the dehydrated versions both look very similar, even under a microscope.

Note¹: To all the chemists and physicists out there: yes, it's an endless debate whether boiling an egg is chemistry or physics... ¯\_(ツ)_/¯