Read Acts 10, the full account of Cornelius. This is a turning point in the work of the apostles. Verse 2 says Cornelius was a devout and God fearing man before he met Peter. He was saved before he called for Peter but he needed instruction in how Christians are supposed to live. He didn't know the details about Christ. He did know about Christ, though. Go down to v32 and 33. Both verses start with 'you know that...' Cornelius knew about Christ and with his devotion was saved. He was what Paul later referred to as a baby Christian who needed milk but still, he was definitely saved and the Spirit could have come on him at any time.
However, God was holding off with the Spirit until Peter was there. This was a lesson for Peter more than for Cornelius. Peter needed instruction in how to deal with Gentile converts. He'd just experienced his vision with sheet full of unclean thing but didn't know how to apply it. Now Peter fully understood. This was God's lesson to him that Gentiles could be saved and Spirit filled just like the Jews. After this lesson, Peter's attitude and actions changed completely. He was now ready to go out among the Gentiles and to accept Paul's calling as being from the Lord.
The Case of Cornelius is an interesting study. Dr. Luke actually discusses the "full account" in Acts 10, 11, and 15.
Acts 10 is what one could call the general account told by Dr. Luke. Acts 11 is the same account, told by Peter, "by order" . . . or one might say he told them what happened in the chronological order of events.
Luke tells us that Cornelius was devout man in the eyes of the Jews, but he was lost.
Look at what Cornelius told Peter when he arrived, with regards to what the angel had said unto him . . .
Acts 11: 14-15
14
Who shall tell thee words, whereby thou and all thy house shall be saved. It was the words that Peter was to deliver that had the power to create saving and obedient faith in Cornelius.
But Peter and the six Jewish Christians of the Circumcision, that accompanied him to the house of Cornelius, need to be convinced that Cornelius was worthy to hear the Gospel. That is why God sent the Holy Spirit directly from heaven, rather than by the laying on of an Apostle's hands (such as Peter and John Acts 8:18)
15
And as I began to speak, the Holy Ghost fell on them, as on us at the beginning...
Since faith comes by hearing the word of God (Rom 10:17) and the Holy Spirit fell on the household of Cornelius before he heard the word, then we can conclude that this miraculous falling of the Spirit had nothing to do with his salvation. The Gospel is the power of God unto salvation (Roman 1:16)
So it is clear, that once the six Jewish brethren and Peter saw that Cornelius and his household had received the Holy Spirit directly from heaven, as had he and the other Apostles (Acts 2:1-4) they were convinced the Gentiles were accepted by God (Acts 11:16-18; 15:7-9) and received salvation through faith and obedience to the Gospel command to be baptized (Acts 10:47-48)
Even if Cornelius wasn't saved when Peter arrived, 'when Peter began to speak' is actually the following verses:
34 ¶ Then Peter began to speak: "I now realise how true it is that God does not show favouritism
35 but accepts men from every nation who fear him and do what is right.
36 You know the message God sent to the people of Israel, telling the good news of peace through Jesus Christ, who is Lord of all.
37 You know what has happened throughout Judea, beginning in Galilee after the baptism that John preached—
38 how God anointed Jesus of Nazareth with the Holy Spirit and power, and how he went around doing good and healing all who were under the power of the devil, because God was with him.
39 "We are witnesses of everything he did in the country of the Jews and in Jerusalem. They killed him by hanging him on a tree,
40 but God raised him from the dead on the third day and caused him to be seen.
41 He was not seen by all the people, but by witnesses whom God had already chosen—by us who ate and drank with him after he rose from the dead.
42 He commanded us to preach to the people and to testify that he is the one whom God appointed as judge of the living and the dead.
43 All the prophets testify about him that everyone who believes in him receives forgiveness of sins through his name."
44 ¶ While Peter was still speaking these words, the Holy Spirit came on
all who heard the message.
Peter gave them a full salvation message before the Spirit came on them in V 44. They already knew who Jesus was, verses 36,37, and Peter gave them vital information. Whether before or after Peter arrived, they got the full message and believed. Somewhere in this before the Spirit came, they accepted Christ. The Spirit didn't come on unsaved people.
