The gospel is the power of God unto salvation. If he sends for Peter and hears the message and believes on the Christ of that message then he WILL be saved. And if he does not he won't be. This surely is why the whole story is built around God's miraculously getting Cornelius and Peter together. Cornelius had to hear the gospel message to be saved.
Forgiveness of sins is salvation.
No one is saved whose sins against God are not forgiven by God. And Peter says that forgiveness comes through believing in Christ, and it comes through the name of Christ. So again it is very unlikely that verse 35 means that Cornelius and his household were already forgiven for their sins before they heard the message of Christ. Elsewhere in the book of Acts even those who are the most God-fearing and ethical, namely the Jews, are told that they must repent and believe in order to be saved. So Luke is not trying to tell us in this book that devout, God-fearing people who practice what's right as best they know how are already saved and without any need of the gospel.