I keep disagreeing that you’d understand all of the New Testament. Mark and John, sure; Paul, not so much.
Byzantine learned literature: forget it. It’s not identical to Attic Greek, but you’ll need Attic Greek (and a decoder ring) to make sense of it.
Byzantine Vernacular literature (1100 onward): sure, but knowing some dialect, e.g. Cypriot or Cretan will help a lot.
Attic. No. Worse, you’ll think that you understand it, and you’ll be wrong.
Homeric. As I love to say, it might as well be Albanian.