Not according to this book:
Robinson thinks that the 4th gospel included information gleaned from an independent eyewitness source whose knowledge of Jerusalem has subsequently been shown to be reliable by archaeologists.
Of course, that in itself is not sufficient to demonstrate that John preceded Mark, and unfortunately I can't recall how Robinson builds his case for that, or whether he thinks of the gospel as being the handiwork of one author (which seems highly implausible), as it is now more than 30 years since I was alerted to this publication and I never got around to reading it.
But I still have it and might have a go at it at some point. The synoptic problem and the quest for the historical Jesus can be fascinating even if, like me, you don't believe in the God of classical theism.
The thing that amazes me is how some Christians consider the Bible to be a piece of dictation from God, as evangelicals and fundamentalists do, as this is surely the equivalent of believing that the earth is flat.