Remember, the Lord's body did break down and Simon the Cyrene was compelled to carry the cross on the way to the place of the Skull. I believe He chose that break down to prophesy the destruction of Rome in 70AD warning graciously the women of Jerusalem the horrors to come and results of rejecting their King (remember the sign above the Cross - King of the Jews).
No, he did not faint on the Cross, doing the work of saving folks like you and me from ourselves, from death, eternal hell and ultimately the second death.
And giving his mother to St. John (and for us), for he had no brothers or sisters.
AMEN