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No way! An easy example is the centroid and circumcenter of a right-angle triangle. Circumcenter will be exactly on the middle of the hypotenuse which obviously cannot be the centroid.

Centroid is the point where all three lines are connecting all the three vertices and the middle of the line opposite the respective vertex.

Circumcenter is the center of the circle passing through all the vertices. As it is known, a right-angle triangle will always fall within a semicircle, meaning the circle center will always be on the middle of the hypotenuse.

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Q: Is the centroid of a triangle always the circumcenter of a triangle?
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