Is it possible to use Prodigy with text that is in Greek? Will I have to do something special to be able to work with Greek text? (There is a Spacy Greek model, although it performs rather awfully when it comes to NER and that mandates some custom training )
Prodigy itself is pretty agnostic to what text you load into it people are using it with text in all kind of languages and writing systems. So there's nothing specific you'd have to do to make it work for Greek – if you want to use the built-in recipes, you'd just use blank:el or the pretrained Greek model as the base model. The only things you have to decide is what you want to label, whether you want to start with a pre-trained model and how you want to update it.
That model was actually developed as part of a Google Summer of Code project and the team used Prodigy to hand-annotate a small NER corpus completely from scratch using Prodigy (since there wasn't any other suitable data available) 
If you like the categories and just want to improve them, a workflow like ner.correct where you correct existing predictions could be a good start.