Hi, Kelly –
I haven’t seen the complete blue-covered book, but I believe most of the content will be the same. I would think you can use it.
The main portion I would want to make sure was in the blue-covered book was the first few paragraphs of the chapter called “The Gods of Greece.” Those introductory paragraphs explain how their myths didn’t actually happen, as well as the difference between myths and legends. You might want to make sure those paragraphs are included. I think they are very important for our children’s understanding.