No, I would not agree. From the Catholic Encyclopedia:
Testament come from testamentum, the word by which the Latin ecclesiastical writers translated the Greek diatheke. With the profane authors this latter term means always, one passage of Aristophanes perhaps excepted, the legal disposition a man makes of his goods for after his death. However, at an early date, the Alexandrian translators of the Scripture, known as the Septuagint, employed the word as the equivalent of the Hebrew berith, which means a pact, an alliance, more especially the alliance of Yahweh with Israel. In St. Paul (1 Corinthians 11:25) Jesus Christ uses the words "new testament" as meaning the alliance established by Himself between God and the world, and this is called "new" as opposed to that of which Moses was the mediator. Later on, the name of testament was given to the collection of sacred texts containing the history and the doctrine of the two alliances; here again and for the same reason we meet the distinction between the Old and New Testaments. In this meaning the expression Old Testament (he palaia diatheke) is found for the first time in Melito of Sardis, towards the year 170. There are reasons for thinking that at this date the corresponding word "testamentum" was already in use amongst the Latins. In any case it was common in the time of Tertullian.
The pact or alliance began when?
The first chapter of Luke provides the answer.
Luke 1: 5 2 In the days of Herod, King of Judea, 3 there was a priest named Zechariah of the priestly division of Abijah; his wife was from the daughters of Aaron, and her name was Elizabeth. 6 Both were righteous in the eyes of God, observing all the commandments and ordinances of the Lord blamelessly. 7 But they had no child, 4 because Elizabeth was barren and both were advanced in years. 8 Once when he was serving as priest in his division's turn before God, 9 according to the practice of the priestly service, he was chosen by lot to enter the sanctuary of the Lord to burn incense. 10 Then, when the whole assembly of the people was praying outside at the hour of the incense offering, 11 the angel of the Lord appeared to him, standing at the right of the altar of incense. 12 Zechariah was troubled by what he saw, and fear came upon him. 13 But the angel said to him, "Do not be afraid, 5 Zechariah, because your prayer has been heard. Your wife Elizabeth will bear you a son, and you shall name him John. 14 And you will have joy and gladness, and many will rejoice at his birth, 15 for he will be great in the sight of (the) Lord. He will drink neither wine nor strong drink. 6 He will be filled with the holy Spirit even from his mother's womb, 16 and he will turn many of the children of Israel to the Lord their God. 17 He will go before him in the spirit and power of Elijah 7 to turn the hearts of fathers toward children and the disobedient to the understanding of the righteous, to prepare a people fit for the Lord." 18 Then Zechariah said to the angel, "How shall I know this? For I am an old man, and my wife is advanced in years." 19 And the angel said to him in reply, "I am Gabriel, 8 who stand before God. I was sent to speak to you and to announce to you this good news. 20 But now you will be speechless and unable to talk 9 until the day these things take place, because you did not believe my words, which will be fulfilled at their proper time." 21 Meanwhile the people were waiting for Zechariah and were amazed that he stayed so long in the sanctuary. 22 But when he came out, he was unable to speak to them, and they realized that he had seen a vision in the sanctuary. He was gesturing to them but remained mute. 23 Then, when his days of ministry were completed, he went home. 24 After this time his wife Elizabeth conceived, and she went into seclusion for five months, saying, 25 "So has the Lord done for me at a time when he has seen fit to take away my disgrace before others."
26 10 In the sixth month, the angel Gabriel was sent from God to a town of Galilee called Nazareth, 27 to a virgin betrothed to a man named Joseph, of the house of David, and the virgin's name was Mary. 28 And coming to her, he said, "Hail, favored one! The Lord is with you." 29 But she was greatly troubled at what was said and pondered what sort of greeting this might be. 30 Then the angel said to her, "Do not be afraid, Mary, for you have found favor with God. 31 Behold, you will conceive in your womb and bear a son, and you shall name him Jesus. 32 He will be great and will be called Son of the Most High, 11 and the Lord God will give him the throne of David his father, 33 and he will rule over the house of Jacob forever, and of his kingdom there will be no end." 34 But Mary said to the angel, "How can this be, since I have no relations with a man?" 12 35 And the angel said to her in reply, "The holy Spirit will come upon you, and the power of the Most High will overshadow you. Therefore the child to be born will be called holy, the Son of God. 36 And behold, Elizabeth, your relative, has also conceived 13 a son in her old age, and this is the sixth month for her who was called barren; 37 for nothing will be impossible for God." 38 Mary said, "Behold, I am the handmaid of the Lord. May it be done to me according to your word." Then the angel departed from her.
So when did the pact begin?
Jesus told you when it began and you prefer the Catholic encyclopedia ..what can I say ?
A covenant has no value if it is never signed..
Hbr 9:15 And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions [that were] under the first testament, they which are called might receive the promise of eternal inheritance.