In a word: yes! Read what Tim Brister has to say on the subject:
Is the call to evangelize the lost something that all Christians are expected to engage in? This is a question that was recently raised to me. I certainly don’t think it will look the same way with each person, but I do believe we are all called to witness for Christ and live evangelistic lives commending the gospel to others in word and deed. As I reflected on this, four verses began to surface in my thinking about how Paul shows the necessity of evangelism:
I am under obligation both to Greeks and to barbarians, both to the wise and to the foolish. So I am eager to preach the gospel to you also who are in Rome.
Romans 1:14-15
I have great sorrow and unceasing anguish in my heart. For I could wish that I myself were accursed and cut off from Christ for the sake of my brothers, my kinsmen according to the flesh.
Romans 9:2-3
For if I preach the gospel, that gives me no ground for boasting. For necessity is laid upon me. Woe to me if I do not preach the gospel!
1 Corinthians 9:16
Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God.
2 Corinthians 5:20
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