When you say "the conquest" do you only mean the part where Joshua and Israel invaded the lands west of the Jordan river? Or do you include their conquests east of Jordan under Moses?
To me, it appears that Israel's intent was to exterminate all the descendants of Canaan ("Canaanites"). They attacked the Amorites in their homeland (east of Galilee in the hill country) and seized all their cities, probably in the 14th century BC. So if I must give a straight yes/no answer, it's YES.
On the other hand, by the end of Exodus there are places where nations are listed together as "Canaanites, Amorites, Jebusites, Hivites," etc. I attribute this to the Torah having been compiled centuries later by editor(s) who made that distinction. Depending on how you view the genesis of... well... Genesis... you may have a different view. Theologians and Scholars do NOT agree on this AT ALL.
For the purposes of this topic, it's probably worth noting that by New Testament times, a lot of the "Canaanites" living in "Canaan" probably weren't actually descended from Canaan. The Luwian "Sea Peoples" overtook most of the city-states along the coastline in the 12th century BC, and were probably descended from Japheth rather than Ham/Canaan. They also intermarried with the Hittites further north.
Later they all were conquered by the (neo-)Assyrians, who were Semites. The Israelites never accomplished God's mandate to eliminate the Canaanites, but the Assyrians may have. They certainly cut a bloody swath through the whole area.
-Jarrod
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