Without this chapter, the biography of Abraham would still appear to be complete. However, we would have a slightly rosier portrait of Abraham; we wouldn't see the connection with Isaac's behavior in Genesis 26 (he ends up doing the same thing his Dad did) and we wouldn't have as much of a whole history between the Jews and the Philistines.
Abraham, in an attempt to save his own skin, is (again) guilty of cowardly, faithless and unchivalrous deception. You would think Abraham would have learned his lesson when this same strategy (Genesis 12:13) failed down in Egypt. But, no...it is recorded that he attempted the same thing with King Abimelech that he had attempted with the Egyptian Pharaoh.
This time God appeared to the king in a dream and warned him concerning Sarah (Genesis 20:3). Abraham had assumed that this king was a godless man (Genesis 20:11), but evidently this wasn't the case (Genesis 20:4 & 6). In fact, king Abimelech and his household demonstrated a proper fear of God, a respect for the prophet Abraham and a generous spirit toward God's chosen family.
I do find it interesting that Abraham's partial truth (Genesis 20:12) was judged to be a complete lie... despite the fact that - in his reproof of Abraham and his wife - the king used a little bit of sarcastic humor, calling Abraham "Sarah's brother" instead of her husband (Genesis 20 :16).
Happily, in the end, God's sovereign grace prevailed. We find His elect friend Abraham praying successfully for Abimelech's healing and for the healing of his whole house, not vice versa.