I don't think this example is so clear. First, "logos" is a common word that appears hundreds of times in the NT. Second, "the word of God / the LORD" is a common and important occurrence in the OT. John's argument is that Jesus was the one delivering these messages, as he existed beforehand to do so (see John 8:52-58).
Third, just because it was a Greek concept, doesn't mean John is intending to apply it here. An easy example is how the Septuagint always translates the Hebrew word "sheol" to the Greek word "hades". Even though hades is a Greek philosophical concept, the intention is not to apply that concept; it's just the word that the translators decided is closest to the meaning of the original.
With that said, there's no question that the early church beyond the twelve wrestled with and eventually incorporated many Greek philosophical concepts into their belief systems. We just don't see clear evidence of that in the gospels, I don't think.
Ultimately, I’ve found that a person’s opinion on this tends to follow their preconceived ideas. Someone intending to dismiss Christianity altogether might conclude that since its supernatural claims are probably untrue then the whole thing should be thrown away. On the other hand, someone intending to take Christianity seriously might find that the combination of its founder’s teaching plus three thousand years of cultural development is something of extraordinary value in itself, regardless of any faith in the supernatural.