Does this passage refute the necessity of Baptism for Salvation?

Of course he was sent to baptize as that is part of the Great Commission, a part which he administered personally and/or through those that accompanied him. However, the issue here is one of emphasizing baptism and the baptismal administrator above all else so that the church is split into party divisions over baptism. It is in this sense, he was not sent to baptize. The gospel takes precedence over baptism.

However, in demonstrating that the gospel takes precedence over baptism this text most certainly does repudiate baptismal regeneration in several ways. First, he is directly comparing the superiority of the gospel to baptism with regard to the power of God in salvation. He directly attributes the power of salvation to the gospel rather than to baptism. Hence, this repudiates baptismal regeneration as baptismal regeneration would make the power of salvation inclusive with baptism.

Moreover, it repudiates baptismal regeneration most emphatically by the fact that Paul is addressing specifically what Christ sent him to do with regard to the gospel in contrast to baptism. He says here "Christ SENT ME NOT to baptize" while in Acts 26:17-18 we have Christ's own words "Now I SEND THEE to.." with regard to the gospel:

17 Delivering thee from the people, and from the Gentiles, unto whom now I send thee,
18 To open their eyes, and to turn them from darkness to light, and from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me.

A. Christ sent me not to baptize
B. Christ did send him to open their eyes
C. Therefore, their eyes can be opened without baptism.

A. Christ sent me not to baptize
B. Christ did send him to turn them from darkness to light
C. Therefore, they can be turned from darkness to light without baptism

A. Christ sent me not to baptize
B. Christ did send him to turn them...from the power of Satan unto God
C. Therefore, they can be turned from the power of Satan unto God without baptism

A. Christ sent me not to baptize
B. Christ did send him that they may receive forgiveness of sins
C. Therefore, they can receive forgiveness of sins without baptism.

A. Christ sent me not to baptize
B. Christ did send him that they may receive....inheritance among them which are sanctified by faith
C. Therefore, they can receive inheritance among them which are sanctified by faith without baptism

Furthermore, this commission of Christ is interpreted by Paul with reference to the gospel as he continues to say"

22 Having therefore obtained help of God, I continue unto this day, witnessing both to small and great, saying none other things than those which the prophets and Moses did say should come:
23 That Christ should suffer, and that he should be the first that should rise from the dead, and should shew light unto the people, and to the Gentiles.

The gospel provides LITERAL salvation where baptism at best only supplies FIGURATIVE salvation (1 Pet. 3:21).