What would have happened if Israel had accepted Jesus as Messiah? Would Jesus still have died on a cross?
Any consideration of what might have happened had Israel accepted Jesus as Messiah is entirely theoretical, nevertheless, we can make some educated guesses based on what we know of the plan of redemption.
First, Jesus had to die in our place as our propitiation, so if Israel had accepted Jesus as Messiah, He would still have gone to the cross at Passover for Israel's sins and the world. Who would have killed Jesus? We assume the Romans would have done God's bidding without the need for a Jewish conspiracy since the Romans would have naturally been concerned about the threat posed by a Jewish king claiming the throne of Israel.
After three days in the grave, the Messiah would have risen, sat on His throne and judged the world as He will do at His Second Coming. Following that, the Kingdom would have arrived for Israel (but precious few Gentiles would have been included).
So had Israel accepted the offer of the Kingdom, it theoretically could have come in that time, but Jesus would still have died as the Lamb of God.