I am fully aware Scripture says to preach the Gospel. However, if one accepts that Calvinist position that a person is either among the elect or among the damned (and that this determination was made at the foundation of the world), it seems unnecessary.
Under Calvinism is salvation based upon election or is it based upon believing? Now, I understand that some say the elect WILL believe, but wouldn't this happen regardless?
Why would it be "unnecessary" when God tells us the preaching of His word is the ways and means of how the Holy Spirit renews a man's mind to know the things of God?
None of us knows the names of the elect, but God. So we preach the Gospel to all men, confident that those who are His will respond in the true faith God gives them.
Under Calvinism is salvation based upon election or is it based upon believing?
Election is the name for the will and purpose of God which determine who will believe since all men are fallen and none can be righteous unless and until God gives them a new birth by the Holy Spirit which imputes Christ's righteousness to them.
Faith is the evidence of that merciful imputation, the good fruit of the free gift of the indwelling Holy Spirit.
Now, I understand that some say the elect WILL believe, but wouldn't this happen regardless?
Paul answers your question...
For whosoever shall call upon the name of the Lord shall be saved. How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher? And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!" -- Romans 10:12-15" For there is no difference between the Jew and the Greek: for the same Lord over all is rich unto all that call upon him.
The preaching of the word is how God reaches His children. Therefore He instructs us to preach the Gospel to all men and thereby to be confident every one of those children will hear the truth and respond in true and saving faith at a time and circumstance appointed by God for His glory. That assurance is enough for me.
For I came down from heaven, not to do mine own will, but the will of him that sent me. And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day." -- John 6:37=39"All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out.