Yes, Arjuna did violate the celibacy rule of his oath. In one instance (Ulūpī), the reasoning given is: Fulfilling the sexual urges of a woman who will otherwise commit suicide takes precedence over one's oath of celibacy!
Ādi Parva / Arjuna-vanavāsa Parva
One day, when this was going on, the son of Kunti and Pandu entered the Ganga to have a bath. O king! He performed his ablutions and offered water to his grandfathers. He was about to climb out of the water, wishing to perform rites to the fire. O great king! The mighty-armed one was grasped and pulled into the water by Ulupi, daughter of the king of the nagas, who could travel where she willed. There, in the revered palace of the naga named Kouravya, the Pandava saw a fire that had been built up well. Kunti's son Dhananjaya performed his rites in that fire. Witnessing the unhesitating offering of oblations, Hutashana" was satisfied.
After having performed his rites before the fire, Kunti's son smilingly uttered these words to the daughter of the naga king. "O beautiful one! O timid one! How did you perform such a courageous act? What beautiful land is this? Whom do you belong to and whose daughter are you?" Ulupi replied, "O Partha! The serpent Kouravya is descended from the lineage of Airavata. I am his daughter and a serpent named Ulupi. O Kounteya! I saw you descend into the water to have a bath and was robbed of my senses by the god of love. O descendant of the Kuru lineage! The god of love is churning me. I am yet a maiden. Please me today by giving yourself to me."
Arjuna said, "O fortunate one! I have been commanded by Dharmaraja to observe brahmacharya for twelve years and do not have control over myself. O dweller in the water! I do wish to do that which brings you pleasure. But never before this have I spoken that which is untrue. O serpent-maiden! How can I bring pleasure to you and yet not do that which is untrue? How can I not violate dharma?"
Ulupi replied, "O Pandava! I know why you are roaming the earth. I know that you are observing brahmacharya on the instructions of your superior. This was the rule you made among yourselves for Drupada's daughter, that anyone deluded enough to enter would retire to the forest and observe brahmacharya for a period of twelve years. The exile is therefore for the sake of Droupadi. You are observing that dharma. But in this case, dharma does not suffer. O large-eyed one! It is your duty to save those who are distressed. By saving me, dharma is not violated. O Arjuna! Even if there is a slight transgression of dharma, by granting me life, you will achieve greater dharma. O Partha! O lord! I desire you. Desire me in return. That is the view of those who are rigid in their vows. Know that if you do not do this, I will certainly die. O mighty-armed one! Grant me life and achieve supreme dharma. O supreme among men! I am now seeking refuge with you. O Kounteya! You have always protected those who are weak and without protectors. I am miserable and weeping and am seeking refuge with you. I am overcome with desire and am seeking you. Do that which is pleasurable to me. Satisfy my desire by giving yourself to me." Hearing these words Kounteya then did what she wanted, accepting dharma to be the reason. The powerful one spent the night in the palace of the serpent. When the sun rose, he too arose from Kouravya's abode.
[Debroy, Bibek. The Mahabharata: Volume 2 (pp. 15-18)]