Yes, the faithful Catechumen is saved, by virtue of his desire for Baptism.
St. Ambrose of Milan:
"But I hear that you grieve because he did not receive the sacrament of baptism. Tell me: What else is in your power other than the desire, the request? But he even had this desire for a long time, that, when he should come into Italy, he would be initiated, and recently he signified a desire to be baptized by me, and for this reason above all others he thought that I ought to be summoned. Has he not, then, the grace which he desired; has he not the grace which he requested? And because he asked, he received, and therefore is it said: “By whatsoever death the just man shall be overtaken, his soul shall be at rest” (Wisd. 4:7). Grant, therefore, O holy Father, to Thy servant the gift which Moses received, because he saw in spirit; the gift which David merited, because he knew from revelation. Grant, I pray, to Thy servant Valentinian the gift which he longed for, the gift which he requested while in health, vigor, and security. If, stricken with sickness, he had deferred it, he would not be entirely without Thy mercy who has been cheated by the swiftness of time, not by his own wish. Grant, therefore, to Thy servant the gift of Thy grace which he never rejected, who on the day before his death refused to restore the privileges of the temples although he was pressed by those whom he could well have feared. A crowd of pagans was present, the Senate entreated, but he was not afraid to displease men so long as he pleased Thee alone in Christ. He who had Thy Spirit, how has he not received Thy grace? Or if the fact disturbs you that the mysteries have not been solemnly celebrated, then you should realize that not even martyrs are crowned if they are catechumens, for they are not crowned if they are not initiated. But if they are washed in their own blood, his piety and his desire have washed him, also." (Oration at the Funeral of the Emperor Valentinian I)
St. Augustine of Hippo:
"That the place of baptism is sometimes replaced by martyrdom is supported by an argument by no means trivial, which the blessed Cyprian adduces from the thief, to whom, though he was not baptized, it was said, “Today thou shalt be with me in paradise.” On considering which, again and again, I find that not only martyrdom for the sake of Christ may supply what was wanting of baptism, but also faith and conversion of heart, if recourse may not be had to the celebration of the mystery for want of time. For neither was that thief crucified for the name of Christ, but as the rewards of his own deeds; nor did he suffer because he believed, but he believed while he was suffering. It was shown, therefore, in the case of that thief, how great is the power, even without the visible sacrament of baptism, of what the apostle says, “With the heart man believes unto righteousness, and with the mouth confession is made unto salvation.” But the want is supplied invisibly only when the administration of baptism is prevented, not by contempt for religion, but by the necessity of the moment." (On Baptism against the Donatists, Book IV, 22)