This passage is one people seem to use often in defense of the idea of a pro-military Jesus. As one example, we've got this reply to my first student opinion article. But enough of that. Let's look at what the text of Luke 7:1-10 (NIV) says:
When Jesus had finished saying all this in the hearing of the people, he entered Capernaum. There a centurion's servant, whom his master valued highly, was sick and about to die. The centurion heard of Jesus and sent some elders of the Jews to him, asking him to come and heal his servant. When they came to Jesus, they pleaded earnestly with him, "This man deserves to have you do this, because he loves our nation and has built our synagogue." So Jesus went with them.
He was not far from the house when the centurion sent friends to say to him: "Lord, don't trouble yourself, for I do not deserve to have you come under my roof. That is why I did not even consider myself worthy to come to you. But say the word, and my servant will be healed. For I myself am a man under authority, with soldiers under me. I tell this one, 'Go,' and he goes; and that one, 'Come,' and he comes. I say to my servant, 'Do this,' and he does it."
When Jesus heard this, he was amazed at him, and turning to the crowd following him, he said, "I tell you, I have not found such great faith even in Israel." Then the men who had been sent returned to the house and found the servant well.
Pretty surprising that Jesus would say that to a Roman centurion. He never seems to praise Jewish freedom fighting guerrilla groups. In fact, the New Testament almost never mentions any of those groups. But Jesus says a good thing about a Roman soldier. And Luke specifically writes favorably about the Romans.
In chapter 7 Jesus helps a Roman soldier with a sick slave. Immediately after that incident Jesus raises a widow's son. In short, Jesus is exemplifying what it means to live by Leviticus 19:32-34 (NIV),
Rise in the presence of the aged, show respect for the elderly and revere your God. I am the LORD. When an alien lives with you in your land, do not mistreat him. The alien living with you must be treated as one of your native-born. Love him as yourself, for you were aliens in Egypt. I am the LORD your God.
Thus, we see a very inclusive concern for others in Jesus' actions. The centurion also serves as an ironic contrast in faith with John the Baptist later in the chapter. Luke uses the lowly for ironic contrasts often enough, such as in Luke 18. That chapter has a widow seeking justice and an apathetic judge. Justice happens because of a poor helpless old woman. The Pharisee and tax collector is yet another such contrast. The following episodes about the little children and the rich ruler both have their own contrasts, but they're less obvious.
Note that nowhere is the centurion said to become a disciple. Jesus heals those who turn to him, and that's that. In Luke 5:12-26 we have two episodes of healings that did not necessarily lead to discipleship. The man possessed by Legion in Mark 5 was not allowed to be a disciple, but was told to go back and be with his family (5:18-20).
Healing/miracle stories do not concern themselves with whether a healed person ends up living "happily ever after." The focus is on what Jesus said and did. As far as what happened to the person healed, the only things reported are (usually) the fact that healing did happen and that people were amazed in response. Therefore, we can't really say at all that this centurion became a disciple. Besides, a Roman centurion can't just quit his job and convert to Judaism and follow a Rabbi around. Going AWOL (or just displaying cowardice at all) was punishable by death.
And lastly, let me add this. People are willing to use this as a prooftext for saying Jesus approves of soldier-disciples, but nobody seems to notice the same logic could use this passage to approve of slavery. This slaveholder was not told to free his newly-healed slave either, as the text has it. So, if this passage proves that Jesus was not non-violent, it also "proves" slavery is perfectly acceptable in God's eyes.
I don't like slippery slopes, but I dislike double standards even more. People are inconsistent and use whichever interpretive style fits the point they want the text to make. Ugh.