It certainly could but this raises a number of issues. Just to spitball some of them:
-
Half of critics think John had direct literary dependence on Mark. Half doesn’t. Thus, if Mark is not Peter’s testimony and the author of Mark also did a little framing, many will ask why does an eyewitness to it all use non-eyewitness testimony in constructing a Gospel?
-
Most of critical scholarship rejects traditional authorship. There are quite a few Gospels claiming to be from people they are not. Most of scholarship also rejects that Paul wrote all the letters in the NT attributed to him despite them claiming to be written by him explicitly. I think Bird and Wright actually settled for John the Elder, not Apostle John. Which brings up the next point.
-
People with the same name were mixed up in antiquity by the Church. Could it have been a different John who may have been present for some of Jesus’ ministry but not all?
-
Its very probable John had more than one author. Chapter 21, where the claim to authorship by a disciple resides, was a redacted second ending. John clearly ends at. 20. Did the first edition make any claim to authorship? If it was redacted the gloss in ch. 19 could be secondary as well. Many scholars point out that John clearly has two endings and some other material appears out of place in the text. It actually looks like some of it was mixed up. Christians in the early church up to the present times have been trying to figure this problem tout.
-
Later followers in a Johannine community could write down a work and attribute it to John even after he died. Because he founded the community and they were based on his teachings and they were disciples of his, this was seen as a legitimate practice. Even if their beliefs evolved a little bit. They could keep the name. This could have happened with Matthew and Q explaining Papias’ otherwise problematic comments about GMatthew. But anyways, this complicates authorship a lot. We are clearly dealing with a community in this case.
-
Most scholars recognize that while much of the material in John is historical or has one at its core, some of it actually looks earlier than some stuff in the synoptic gospels. GJohn shows a good awareness of historical things as well.
-
is the beloved disciple a real person or a literary creation symbolizing the perfect follower of Jesus who doesn’t leave him even at the cross (IIRC taking this literally is in conflict with the Synoptics who say they all left him)?
-
Most people think an eyewitness means it must be biographical. Most scholars feel internal contents show John is not that. Admittedly, it is not impossible for me to surmise an original follower of Jesus filled with the spirit, 50 years later in his old age, wrote a Gospel filled with history, mystery and midrash. To admit the latter is really to make the claim that all we can go by is external attestation which in several cases, makes mistakes in regards to the Gospels.
-
The date of John (75-110), at least the final version, makes authorship by disciples in a community established by John more likely than the apostle himself.
-
The external attestation is clearly in favor of John but there also seems to be a bit of uneasiness in some of them as well.
-
Acts 4 names John uneducated and ordinary. Even without this reference we could surmise a Galilean fisherman could not read or wrote in Greek. He could have had someone write for him but many will find difficult seeing a poor, ordinary fishermen from Galilee dictating a work of art like the Gospel of John in Greek. Scholars would probably be able to determine if the Greek text was a direct translation of Aramaic dictation.
If I had to bet I would guess John establishes a community. After his death a disciple of his writes the Gospel. Then later, apologizing for mistaken eschatological predictions, John is redacted by another follower in the community.
No certainty but I think it accounts for a lot of the data.