Though Othello says he'll "see before" he doubts, he does not follow through with this assertion. Othello's tragedy is based in his jealousy and his misplaced faith in the wrong people. Othello trusts Iago, who seeks his destruction, above those who are actually loyal to him, most importantly his wife, Desdemona. Iago is able to convince Othello of Desdemona's infidelity, and Othello's intensifying jealousy prompts him to then murder her at the end of the play.
With that in mind, this line, spoken in act 3, scene 3, is certainly relevant when discussing Othello's themes. On the one hand, it's obvious that Othello fails to put his words here into action, given that Desdemona herself is entirely innocent against his charges. Even so, he believes the worst of her regardless and goes so far as to murder her in response.
That being said, Othello's statement can itself be put under question and labeled as self-failing on its own terms. After all, Othello's statement of trust is a conditional one. He is, in essence, stating, "I will trust in my wife until I see evidence otherwise," but this statement betrays his own insecurity on the question. After all, someone truly secure in their relationship and trusting in their partner should see no need to investigate their partner's faithfulness to begin with. Thus, the very statement, in and of itself, can be understood as an admission of mistrust on Othello's part. He already doubts his wife.