It seems like a valid argument. If God irresistibly saves sinners without the need for human effort, and if Salvation is all up to Him, then why do we need to spread the Gospel? God does all the work anyway, so what are we here for?
There are several things I want to look at in regards to this objection.
First of all, even if there was no point in evangelism, we should do it anyway, just because God tells us to. I've actually met Calvinists who believe that evangelism has no real purpose or use except as a means for believers to show obedience to God's command to spread the Gospel. I do not share this view, but if there was no point to evangelism, we should do it anyway, for the simple reason that God commands it. "And He said to them, ‘Go into all the world and preach the gospel to every creature." (Mark 15:16)
Secondly, I believe that God commands us to spread the Gospel because we are the tools that uses to do so. Yes, God does all the work in salvation, and He does it irresistibly, but He does it through the Gospel, which He spreads via the mouths of believers.
The only thing that galls me more than a believer taking credit for their salvation is when they take credit for the salvation of others. Paul tells us very clearly that when it comes to spreading the Gospel, "I planted, Apollos watered, but God gave the increase. So then neither he who plants is anything, nor he who waters, but God who gives the increase." (1 Corinthians 3:6-7)
Paul and Apollos both worked hard to spread the Gospel, but in the end, it was God who brought about the increase. "Unless the Lord builds the house, They labor in vain who build it; Unless the Lord guards the city, The watchman stays awake in vain." (Psalm 127:1) In the same way, I would say that unless God is at work through evangelism, it is pointless. No amount of human wisdom and eloquence could ever convert an unbeliever. It takes the power of Christ working within their heart to make that person a "New Creation."
Thirdly, the idea that Calvinism smothers evangelism is simply absurd, and defies history. Many historians and Pastors would agree that Calvinism has done more for evangelism than any other "branch" of Christianity! But don't take my word for it, take a look at this amazing list of great missionaries and evangelists who were Calvinists. You might be surprised at how many names you know and love, but never knew were Reformed!
I want to end with a quote from Pastor David Shrock:
I highly recommend that you listen to the full sermon this quote is from."For Paul, election and evangelism are not at odds. For Paul, election is the motivation that drives him to go share the gospel in all places, the hardest places, because he believes that when the gospel is shared, the voice of Christ will be spoken, the sheep [elect] will hear the voice, and they will follow after Him. He's not saying that they are saved before the foundation of the world. He's not saying that salvation will come without the preaching of the gospel. He is saying that when the gospel is preached, he has absolute confidence that it will be effective, because he knows that there are elect ones out there... in this understanding, election does not hinder evangelism. It energizes it."