Can foods with high sugar content go into GEME?

Yes. 

We won't be demanding what foods you should or shouldn't put in, or in what ratio, that would defeat the purpose of GEME to make life simpler. 

The first bag of GEME-Kobold we provide to you has moisture-adjusting ingredients in it, and it does a great job of neutralizing the carbon-to-nitrogen ratio of the compost, so as long as it's not a lot of stuff with too much broth, not overly viscous and thick go ahead and put it in.