The short answer is “not necessarily”.

“Conscious” denial of the Gospel is not the same thing as denial “with full knowledge.”

“Grave matter” vs. “mortal sin”

In Catholic moral theology, a distinction is made between the objective gravity of an action, and a person’s subjective culpability.

For example (to name an action that everyone agrees is gravely disordered), killing an innocent person is clearly gravely wrong. It is possible, however, that the perpetrator of the crime not responsible, or not fully responsible, for his actions (if, for example, his is not mentally competent).

When the action itself is gravely disordered (gravely immoral), in Catholic terminology, it is called grave matter for sin. (See Catechism of the Catholic Church [CCC] 1858.)

For such an action to be a mortal sin (that is, for the person to be fully responsible for that action), three conditions must be met:

• The matter must be grave (i.e., the action committed must be, objectively speaking, gravely immoral).
• The person must fully understand what he is doing.
• The person must freely and deliberately perform the action.

(See CCC 1857, more fully explained in nos. 1859-1861.)

Hence, someone who honestly and innocently does not know that a certain action is wrong, or acts, say, out of grave fear, then he is not fully responsible for that action (and might even be completely free from responsibility in certain circumstances).

That does not mean that the action itself is not evil; however, determining personal culpability is more complex than simply assessing the objective goodness or evil of an action.

Applied to denying the Gospel

In the scenario described by the O.P., although refusing to believe in the Gospel is certainly grave matter, the person in question is clearly misinformed about the Gospel.

Moreover, there are a number of other factors that probably diminish (and, in my opinion, eliminate) her responsibility:

• Prejudices learned from youth against Christianity. (E.g., if you are taught all your life that Christians are “pagans,” you will have a harder time being convinced by them—and this is not your fault, obviously.)
• Grave fear of the consequences of converting. Regrettably, in most Muslim societies, there is not much tolerance of those who become Christian (and in many cases, it leads to the convert’s exile or death).

In conclusion, then, it is extremely unlikely that her “conscious” denial of the Gospel would be held against her by God.

Not an impediment to salvation, but not a guarantee, either

Note that we are speaking about a person who is (1) gravely misinformed about the Faith, to the point of thinking that it is evil; and (2) in grave fear of converting. In a case like this, the objectively grave matter of refusing to believe cannot be imputed to the person (although it remains grave matter).

Hence, it is not an impediment to the person’s salvation. It is not, however a guarantee of salvation, and in fact, salvation is (at least objectively speaking) harder to obtain, since the person is deprived of all the helps that being a believer entails.

The Church teaches that God gives the opportunity of salvation to all men:

[W]e ought to believe that the Holy Spirit in a manner known only to God offers to every man the possibility of being associated with this paschal mystery (Gaudium et Spes 22).

This is not, of course, a guarantee of salvation, but requires the grace of God and at least the implicit acceptance of that grace on the person’s part, which would require that person, among other things, to behave in accord with his conscience.

For a fuller treatment of the necessity of the Catholic Church for salvation,* and how non-Catholics (and even con-Christians) can be saved, see a document called Dominus Iesus, issued in 2000 by the Congregation for the Doctrine of the Faith, especially Chapter VI, which reads in part:

[I]t must be firmly believed that “the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and baptism (cf. Mk 16:16; Jn 3:5), and thereby affirmed at the same time the necessity of the Church which men enter through baptism as through a door”[Lumen gentium, 14]. This doctrine must not be set against the universal salvific will of God (cf. 1 Tim 2:4); “it is necessary to keep these two truths together, namely, the real possibility of salvation in Christ for all mankind and the necessity of the Church for this salvation” [Redemptoris missio, 9] (No. 20).

[…]

With respect to the way in which the salvific grace of God—which is always given by means of Christ in the Spirit and has a mysterious relationship to the Church—comes to individual non-Christians, the Second Vatican Council limited itself to the statement that God bestows it “in ways known to himself” (No. 21; the quote is from the passage of Gaudium et Spes given above).

* Although it does not directly address the question as asked, it is useful background to address the issue of the contentious dogma Extra ecclesia nulla salus (“Outside the Church there is no salvation.”)

This dogma was first formulated by the Church Fathers of the third century. The Church at the time was conflicted by various heretical and schismatic groups, as well as the pastoral problem of the so-called lapsi (those who caved in to demands to renounce their faith or sacrifice to pagan gods by their persecutors). The first formulation of the dogma appears in the writings of Cyprian of Carthage (d. ca. 258). Hence, Cyprian should be understood to mean, “salvation is not to be found by (deliberately) adhering to heretical or schismatic sects,” but only in the Catholic Church.

This dogma was reaffirmed multiple times, most notably in the Council of Florence, in which the Eastern Orthodox were briefly reunited with the Catholic Church. In the profession of faith Cantate domino, the doctrine is stated as follows:

[The Holy Roman Church] firmly believes, professes and preaches that all those who are outside the catholic church, not only pagans but also Jews or heretics and schismatics, cannot share in eternal life and will go into the everlasting fire which was prepared for the devil and his angels, unless they are joined to the catholic church before the end of their lives.

There are a couple of points to keep in mind here:

• The Council effected a reunion between groups that had previously considered each other schismatic and (to varying degrees) heretical. It would be absurd for each party to affirm that, prior to the reunion, all members of the respective faithful in the opposing camp were destined to eternal condemnation, simply because the reunion had not yet been effected. Hence, there is an assumption in this passage that the refusal to be united to the Church is deliberate.

• It leaves a way out for those who are acting out of invincible ignorance or grave fear: they must be jointed to the Church before the end of their lives. It does not specify the manner in which they are joined, which could be in a way that is extra-sacramental (as with the Catechumens).

(Note that the Church has a long history—dating back at least to Tertullian—of recognizing the so-called “baptism of desire”—the desire of catechumens for Baptism—and “baptism by blood”—that is, the martyrdom of the non-baptized. In other words, those who explicitly desire Baptism but are not able to receive it, and those who give their lives for the Faith, even before their Baptism, can still be saved. See CCC 1257-1261.)

The dogma was given further scrutiny after the discovery of the Americas. (Recall that the Council of Florence concluded in 1449; Columbus set sail in 1492.) Before that time, most Europeans assumed that the Gospel had essentially already been preached to the whole world. It soon became clear, however, that vast numbers of people had simply never been evangelized. Theologians of time (e.g., Francisco de Vitoria and the School of Salamanca) recognized that it was absurd to affirm that the native Americans were condemned simply because they had not been evangelized.

The Church has specifically condemned a “rigoristic” interpretation of this dogma (i.e., that formal membership in the Catholic Church is a strict and absolute requirement for salvation), most notably in a document from the Congregation for the Doctrine of the Faith condemning the rigoristic interpretation of Jesuit Father Leonard Feeney.

Vatican II’s Gaudium et Spes, mentioned above, goes so far as to teach that God offers the possibility (not the guarantee!) of salvation to all men without exception, as mentioned.

The most current authoritative interpretations of this dogma are found in the Catechism of the Catholic Church nos. 846-848 and the document Dominus Iesus mentioned above.

In summary, the Church teaches the following:

• Objectively, all men are obliged to avail themselves of the means of salvation, which includes membership in the Catholic Church.
• Those who are unable to be full members of the Church through no fault of their own (i.e., the usual mitigating circumstances: invincible ignorance, grave fear, etc.) are nevertheless offered the possibility of salvation in ways known to God alone.
• That salvation is in any case mediated through the Catholic Church, even if the person is not initially aware of it. (For Christians, they participate in certain elements of the Catholic Church that are effective for salvation; in particular, they all take part in the one Baptism, and some groups, like the Orthodox, even enjoy all seven Sacraments.)

In this way, we can still affirm that outside the Church there is no salvation, without affirming that God condemns people for actions that are not their fault.