That is not implied. The only thing implied is that the preaching of the gospel is necessary for salvation to occur.
Actually it says its necessary for 'believing' to occur, something YOU ASSUME is impossible apart from an additional irresistible working of grace...one above and beyond the work of grace in the gospel message itself...something the text doesn't even come close to suggesting.
You are simply denying what the text says. It says "NO MAN" not "NO JEW" or "NO HARDENED JEW".
That is because no MAN can come unless they hear, just as Rom. 10:14 affirms. No one is denying the need of all to be drawn, we are denying that that all are being drawn in the context of John 6, because it is NOT UNTIL Christ is raised up from the cross that 'all men are drawn.' If Christ had drawn all men prior to being raised up what might have happened? Imagine if the thousands had come to believe in Christ after his sermon in John 6 as after Peter's sermon in Acts 2. What would that have done? It would have prevented the cross. Jesus had to keep them hardened/blinded for a time.
The gospel is the means of 'drawing,' and the gospel truth is being hidden from their eyes, as they are being sent a spirit of stupor.' AGain, not my words but Christ.
We all are asking, "Why can't Jesus' audience believe?"
Calvinists answer: Because they are born total depraved, meaning unable to see, hear, understand and repent, and God doesn't love them and hasn't chosen to grant them that ability.
Jesus' answer: "
For this reason they could not believe, because, as Isaiah says elsewhere: 40 "He has blinded their eyes and deadened their hearts, so they can neither see with their eyes, nor understand with their hearts, nor turn--and I would heal them." 41 Isaiah said this because he saw Jesus' glory and spoke about him." -John 12:39
And Paul: "" 'Go to this people and say, "You will be ever hearing but never understanding; you will be ever seeing but never perceiving." 27 For
this people's heart has become calloused; they hardly hear with their ears, and they have closed their eyes. Otherwise they might see with their eyes, hear with their ears, understand with their hearts and turn, and I would heal them.' 28 "Therefore I want you to know that God's salvation has been sent to the Gentiles, and
they will listen!"
Jesus also explains why the Jewish leaders of his day couldn't believe in Mark 4 and Matt. 13. Paul likewise in Romans 11.