I'm not sure I know what point you think I was making, so I don't know how to answer that.
Jesus is the "Word" mentioned in these verses. He is also the Christ, hence the Christ was in the beginning, meaning there has never not been a Christ. He didn't have to come to Earth in order for people to have faith in him. In fact, even before his death and resurrection he told people their faith in him had saved them.
Luke 7:50 "Jesus said to the woman, 'Your faith has saved you; go in peace.'"
People saved by their faith in the Christ might be considered Christians, no?
You are mixing up stories. This was the woman who washed Jesus' feet with her tears and poured perfume on them. She was described as a sinner. He told her that her faith had saved her, not healed her.
My bad.
In the text, Jesus is teaching Simon (Lk. 7:44-48). Look at the contrast between the two (Lk. 7:44-46):
You gave me no water - She gave me tears.
You gave me no kiss -- She gives me tender affection.
You gave me no oil - She gives me intimate honor.
Simon failed, the woman passed. The woman had many sins, but now they are forgiven while Simon's sins are retained (Lk. 7:47-48)
This lady lived under a different covenant than we do. Notice that the pardon occurred before the "great commission" of Mark 16:16 was given. Also, while Jesus walked on the earth, there were numerous times he forgave people for different reasons.
You cannot do what this lady did and be forgiven. But, you can be a Christian, which she wasn't at least here.
It's not recored, but if she was alive after the death of Jesus and responded to to the gospel in obedience, she would then be a Christian but not until then.