Does the Calvinistic view of divine sovereignty and freewill undermine evangelistic efforts?

Yes
If God has already predestined those who will come to Him then there is logically no need for evangelism. Romans 10:14 How, then, can they call on the one they have not believed in? And how can they believe in the one of whom they have not heard? And how can they hear without someone preaching to them? We must evangelize otherwise people will not come to know the Lord. God Has given us the responsibility of spreading His message and that is why we must evangelize.

No
Matthew 28:19- Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit.
It comes down to the root of our obedience. Are we called to refrain from sin because of its consequences or are we called to refrain out of obedience to God. By recognizing that
God has called us to preach the Gospel out of obedience rather than His dependence on us we are actually giving Him greater glory. He does not need us to convert others to Him, but rather He has given us the privilege of being His chosen instruments to share the truth of His redemption. Lu 19:40 -He answered, "I tell you, if they were to keep silent, the stones would cry out!" God can handle himself, He doesn’t need us. Also, look at history Charles Spurgeon was a fervent Evangelist. If any person claims Calvinism as reasoning not to evangelize they are merely being disobedient to the scriptures.

Evangelism and theology for the most part go separate ways, and the result is great loss for both. When theology is not held on course by the demands of evangelistic communication, it grows abstract and speculative, wayward in method, theoretical in interest and irresponsible in stance. When evangelism is not fertilized, fed and controlled by theology, it becomes a stylized performance seeking its effect through manipulative skills rather than the power of vision and the force of truth. Both theology and evangelism are then, in one important sense, unreal, false to their own God-given nature; for all true theology has an evangelistic thrust, and all true evangelism is theology in action. - J.I. Packer

I do not come into this pulpit hoping that perhaps somebody will of his own free will return to Christ. My hope lies in another quarter. I hope that my Master will lay hold of some of them and say, "You are mine, and you shall be mine. I claim you for myself." My hope arises from the freeness of grace, and not from the freedom of the will.

CHARLES SPURGEON