Egerton may be to John what Q is hypothetically to Matt/Luke.
Wikipedia cites Jon B. Daniels (The Complete Gospels): "... suggestions that the Egerton Gospel served as a source for the authors of Mark and/or John also lack conclusive evidence. The most likely explanation for the Egerton Gospel's similarities and differences from the canonical gospels is that Egerton's author made independent use of traditional sayings and stories of Jesus that also were used by the other gospel writers."
To be a source for John in the way that 'Q' is believed to be a source for Matthew and Luke, it would have to be earlier than John, which was certainly in existence by the early decades of the second century. The fragments we have are, of course, not the original, and they have been dated paleographically to "not later than 150 CE", then as additional evidence came to light, the end of the second century. The original text could be from the first century and therefore predate John, but there is no way to establish this. Where the similarities to John exist, the less developed form of its traditions is consistent with being a source, but it is also consistent with being a parallel development of earlier traditions that the author of John polished.
Has it been considered that Egerton could in fact be the lost Q source?
First of all, there is no suggestion that the author of John's Gospel ever used Q, yet there are parallels between Egerton and John 5:39-47,10:31-39.
Conversely, neither Matthew not Luke contains any material that parallels John 5:39-47,10:31-39. It seems unlikely, if the two synoptic evangelists were copying from the Egerton gospel, that they would both omit the two passages, about Moses and the intention to stone Jesus.
The 'Q' gospel was a sayings gospel, much like the rediscovered Gospel of Thomas. They contained sayings attributed to Jesus, but no context or narrative, and it is for this reason that Matthew and Luke sometimes contain the same saying but in different contexts or with different narratives. Although the tiny Egerton fragments are sometimes referred to as part of a sayings gospel, I believe there is enough there to properly class it as a narrative gospel, like the four New Testament gospels. For example: "And Jesus said unto the lawyers ... And turning to the rulers of the people he spake this saying ..." or "And the rulers sought to lay their hands on him that they might take him." If Egerton is a sayings gospel, it could be related to Q, either as a source for Q or derived from Q, but if it is a narrative gospel, it is more likely derived directly or indirectly from the narrative gospels that we know.
Returning to Wikipedia, it cites conservative scholar Craig Evans, who believes Egerton draws from the other Gospels just as Justin Martyr did. It was not Q and has no direct relationship to Q.