Yes. The mixing of the water and wine in the chalice before its consecrated is required. While failure to add the water is illicit, it does not affect the validity of the sacrament.
What makes this act significant is what it represents: the water is Christ’s humanity and the wine his divinity. The mingling of the water and wine in the chalice symbolizes the Incarnation of Christ. It also recalls Christ’s Passion when the soldiers pierced his side with a spear and out flowed blood and water (John 19:34), thus signifying baptism and Eucharist.
The act of co-mingling the water and wine for the sacrifice was a practice of the early Church. St. Cyprian of Carthage (A.D. 250) writes in his epistle about the significance of mixing the water and wine:
Because Christ bore us all, in that he bore our sins, we see that by the water, people are signified, while in the wine, indeed, the blood of Christ is shown. And when the water is mixed with the wine in the cup, the people are made one with Christ, and the multitude of believers is coupled and joined to him in whom it believes (W.A. Jurgens, The Faith of the Early Fathers, Vol. 1, 232)
St. Thomas Aquinas in his Summa Theologica (art. 6) answers the question about whether water should be mixed with the wine:
Water ought to be mingled with the wine which is offered in this sacrament. First of all on account of its institution: for it is believed with probability that our Lord instituted this sacrament in wine tempered with water according to the custom of that country: hence it is written (Proverbs 9:5). Pope Alexander I says (Ep. 1 ad omnes orth.): “In the Lord’s chalice neither wine only nor water only ought to be offered, but both mixed because we read that both flowed from his side in the Passion.” Thirdly, because this is adapted for signifying the effect of this sacrament, since as Pope Julius says (Concil. Bracarens iii, can. 1): “We see that the people are signified by the water, but Christ’s blood by the wine. Therefore, when water is mixed with the wine in the chalice, the people is made one with Christ.” Fourthly, because this is appropriate to the fourth effect of this sacrament, which is the entering into everlasting life: hence Ambrose says (De Sacram. v): “The water flows into the chalice, and springs forth unto everlasting life.”