Let's, for the sake of argument, assume that the author of the Qur'an had "too much" knowledge of Greek. It's not just the author that is at stake here. The audience also matters. The Author put in an Arabic approximation of a word that sounds like what John reported for Jesus.
Only so that one day, a 17th century European polemicist (Ludovico Maracci) would finally make the connection that ʾAḥmad must refer to Jesus' Pereclete.
All the while, the actual AUDIENCE was completely in the dark for over a millennium.
The amount of bizarre steps you need to take, that no historian could take them seriously.
1. Jesus makes some prediction in Aramaic of a future being.
2. We don't know what word he would have used, it would certainly not have been ʾAḥmad.
3. Since the saying is unique to John, we have absolutely no reason to think that the saying is actually historical.
4. We would have to assume that the Greek version got corrupted in ALL manuscripts, and all evidence was lot of the original periklytos wording.
5. God then comes in and decides that reference not the Greek wording that would have been well-known to anyone who knows Greek, but the original wording John wrote down that nobody knew (and NOT the original wording Jesus used, since he would not have spoken Greek).
6. As a result the reference would have made no sense to anyone listening to the original revelation.
7. In the late 17th century, a European Polemicist while writing a REFUTATION of the Quran, is divinely inspired to understand God's convoluted trilingual pun.
The story is slightly less convoluted if you take God out of the equation. but you guys wanted him in, so...

1. John wrote periklētos
2. At some point this got corrupted to periklytos "famed"
3. Which pre-Muhammadan Christian or Muhammad himself translated to ʾAḥmad.
In this secular scenario, the main issue is step 2 (and that's what
@Sean W. Anthony referred to with "too much Greek"), the word periklytos is extremely rare, so it's rather unlikely that anyone would misunderstand periklētos that way, unless they knew Homer intimately.