Is conversion necessary for the salvation of the elect?

The doctrine of election is not to be viewed as something separate from the goal of election. When we talk about election, we are talking about bringing a certain number of individuals that God has decreed all the way home to glory, purified by the blood of Christ, and regenerated by His Spirit.

So, for example, it is not acceptable to ask whether Saul would be in heaven had he died an hour before he encountered Christ. God not only orders who the elect are, but He also providentially secures the means by which election finds its ultimate fulfillment in the new heavens and new earth. God ordains the means of every aspect of salvation—from election, to regeneration, to faith, to repentance, to perseverance, to final glory. There is no such thing as election that fails to find its fruition because contained within our understanding of election is the final fruition of what that election will bring to pass.