Yes it was because when Arjuna was born after Pandu prays to Indra for an invincible and worldwide-fame son for an year and when Kunti chants the mantra, Indra said he would give an invincible son and gives them a son who is Arjuna and a divine voice said what Arjuna would do in his life.
"After the birth of Vrikodara, Pandu again began to think, 'How am I to obtain a very superior son who shall achieve world-wide fame? Every, thing in the world dependeth on destiny and exertion. But destiny can never be successful except by timely exertion. We have heard it said that Indra is the chief of the gods. Indeed, he is endued with immeasurable might and energy and prowess and glory. Gratifying him with my asceticism, I shall obtain from him a son of great strength. Indeed, the son he giveth me must be superior to all and capable of vanquishing in battle all men and creatures other than men. I shall, therefore, practise the severest austerities, with heart, deed and speech.'
"After this, the Kuru king Pandu, taking counsel with the great Rishis commanded Kunti to observe an auspicious vow for one full year, while he himself commenced, O Bharata, to stand upon one leg from morning to evening, and practise other severe austerities with mind rapt in meditation, for gratifying the lord of the celestials.
So Pandu did rigorous penance and later Indra was gratified.
"It was after a long time that Indra (gratified with such devotion) approached Pandu and, addressing him, said, 'I shall give thee, O king, a son who will be celebrated all over the three worlds and who will promote the welfare of Brahmanas, kine and all honest men. The son I shall give thee will be the smiter of the wicked and the delight of friends and relatives. Foremost of all men, he will be an irresistible slayer of all foes.' Thus addressed by Vasava (the king of the celestials), the virtuous king of the Kuru race, well-recollecting those words, said unto Kunti, 'O fortunate one, thy vow hath become successful. The lord of the celestials hath been gratified, and is willing to give thee a son such as thou desirest, of superhuman achievements and great fame. He will be the oppressor of all enemies and possessed of great wisdom. Endued with a great soul, in splendour equal unto the Sun, invincible in battles, and of great achievements, he will also be extremely handsome. O thou of fair hips and sweet smiles, the lord of the celestials hath become gracious to thee. Invoking him, bring thou forth a child who will be the very home of all Kshatriya virtues.'
Having said that, Kunti later invoked Indra by the mantra given to her by Durvasa and begat Arjuna and the divine voice already tells the destiny and the famous achievements that Arjuna will do in his life.
"Vaisampayana continued, 'The celebrated Kunti, thus addressed by her lord, invoked Sakra (the king of the gods) who thereupon came unto her and begat him that was afterwards called Arjuna. And as soon as this child was born, an incorporeal voice, loud and deep as that of the clouds and filling the whole welkin, distinctly said, addressing Kunti in the hearing of every creature dwelling in that asylum, 'This child of thine, O Kunti, will be equal unto Kartavirya in energy and Siva in prowess. Invincible like Sakra himself he will spread thy fame far and wide. As Vishnu (the youngest of Aditi's sons) had enhanced Aditi's joy, so shall this child enhance thy joy. Subjugating the Madras, the Kurus along with the Somakas, and the people of Chedi, Kasi and Karusha, he will maintain the prosperity of the Kurus. (Surfeited with libations at the sacrifice of king Swetaketu), Agni will derive great gratification from the fat of all creatures dwelling in the Khandava woods (to be burnt down) by the might of this one's arms. This mighty hero, vanquishing all the effeminate monarchs of the earth, will, with his brothers perform three great sacrifices. In prowess, O Kunti, he will be even as Jamadagnya or Vishnu. The foremost of all men endued with prowess, he will achieve great fame. He will gratify in battle (by his heroism) Sankara, the god of gods (Mahadeva), and will receive from him the great weapon named Pasupata. This thy son of mighty arms will also slay, at the command of Indra, those Daityas called the Nivatakavachas who are the enemies of the gods. He will also acquire all kinds of celestial weapons, and this bull among men will also retrieve the fortunes of his race.'