Having studied through A.T. Robertson's A Grammar of the Greek New Testament in the Light of Historical Research page-by-page, I sensed a value in studying Greek outside of the NT in order to understand the Greek in the NT. Clyde Pharr provided valuable insight to this importance:
It is generally recognized that for the best results in the study of the New Testament, students should read a considerable amount of other Greek first. In the whole circle of Greek literature the two authors most important for the student of the New Testament are Homer and Plato. Herodotus informs us that Homer and Hesiod were the chief sources of the Greek popular religion; and certainly one cannot obtain a clear grasp of the forces opposed to Christianity without a good knowledge of Homer and of the hold that Homer had upon the popular mind. If one is to read intelligently the works of the early church fathers, he must be well acquainted at first hand with Homer. It is Homer, Homer's religion, and Homer's gods which recur constantly in their works and which are attacked over and over again as being the bulwarks of the heathen faith which they are striving to supplant. Homer and the ideas he represents are infinitely more important for the student of the New Testament and of the early church than is Xenophon; and if one can study not more than a year or so of Greek before taking up the New Testament, he should by all means have some Homer followed by Plato. Experience has shown that after a year of Homer, students can and do pass with little difficulty into the New Testament. The passage from Homer to Attic, or to Hellenistic, Greek is of course a great deal easier than vice versa, and occupies very little time and effort (Homeric Greek: A Book for Beginners, xxx).