Eden is not required to finish the MSQ. You'll just run into a bit of a weird spot where Thancred and Urianger are still hanging around despite also being back on the Source, because it was all written on the assumption that players would be running it alongside the main story.

Bonus if you never bothered unlocking the ARR extreme primals or the Binding Coil and Urianger is also still hanging out at the Waking Sands in his old outfit.