It must be acknowledged that Calvinists have not only robustly encouraged, engaged, and propagated missions, but have led some of the great mission's and evangelistic movements in the history of the church. Even a cursory glance at the history of missions and missionaries produces a hall of fame filled with Calvinists. It could rightly be argued that Calvinism is not only not a barrier to missions and evangelism, but has actually proven to be a spur to missions and evangelism. In fact, it has often been the driving force in missions.
A belief in predestination does not set aside that commandment from our Lord, and I've never met a Calvinist that believes it should.
I will have to read this later, but the answer to the headline question is an unequivocal NO.
Knowing that God is fully sovereign, and knowing that he has commanded the great commission, and knowing that He uses the foolishness of preaching the gospel to save souls, and knowing that His sheep hear His voice and they follow Him gives Calvinists the courage and confidence to evangelize. I never had the confidence to even try to win souls until I understood grace. For many years I was reluctant to share my faith because I foolishly thought it was somehow up to me and my perfect explanation of the gospel.
The Fuel of Death Defying Missions – David Platt Sermon
http://jamesmirror.com/2012/04/13/fuel-of-death-defying-missions-david-platt-sermon/
“David Platt’s sermon at the 2012 Together for the Gospel (T4G) conference was one of the most popular from the event receiving accolades from John Piper and others. Platt’s basic premise is, “A high view of God’s sovereignty fuels death-defying devotion to global missions” or said another way “pastors who believe that God is sovereign over all things will lead Christians to die for the sake of all peoples.”
Platt’s whole sermon is worth your time.