Would Peter have hesitated to enter Cornelius' house if he understood the gospel of grace?
No. Had Peter understood the gospel of grace, the law-based barrier against keeping company with a Gentile would never have crossed his mind. Instead of hesitating at Cornelius' threshold, he would have been eager—even thrilled—to enter the military officer's house. His words there show he had not yet comprehended that gospel.
Les explains that the Jewish believers in Jerusalem were still basically law keepers and had not comprehended Paul's gospel of grace. Peter's vision of the sheets illustrates that law mindset: he said, "Not so, Lord," because he had never eaten anything common or unclean. At Cornelius' threshold, before entering, Peter told Cornelius it was unlawful for a Jew to keep company with a man of another nation. If Peter had understood Paul's gospel of grace, that would not have crossed his mind; he should have been thrilled to enter the house of a military officer. The law was still bugging him, even though God had made plain this was what He wanted. The same controversy later appeared when Jerusalem emissaries undermined Paul's congregations and challenged his apostleship, but Paul said he needed no official recognition from Peter because his came from the Lord in heaven.