In this poem the seafarer does determine that "Fate" is stronger than man's mind. The answer to this question depends upon the definition of "Fate." In the poem, and especially in a Christian reading, "Fate" is synonymous with God's will. So, if we take Fate to mean the result of God's divine plan, then it makes sense (within this reading of the poem) that Fate/God is stronger than any man's mind, since God's divine plan is irrefutable.
Or, if we understand "Fate" in a Naturalist reading, again, Fate is usually (but not always) stronger than man's mind. In Naturalist literature, a character is the victim of his/her natural and cultural environment. In this poem, it is the seafarer against nature ("the sea took me"). He laments his harsh life at sea, and feels he is at Nature's mercy. At the end of the poem, the seafarer conflates this idea of Nature's control of his fate with the will of God. So, this Naturalist reading goes along with the first reading of Fate as God's divine plan.
This is the reading in the poem, that Fate is stronger than man's mind. It is only when the seafarer accepts his fate (or his role in God's plan), that he loses his fear.
He who lives humbly has angels from Heaven
To carry him courage and strength and belief.
In the end, the seafarer puts most, or all, of his hope in Heaven. He has accepted his fate.
Outside of this poem, the question of fate vs. man, man vs. nature, or the power of free will is more debatable. In terms of Naturalism, the debate boils down to man's ability to determine his future, given the natural and social elements of his environment and place in history.