Has the Catholic Church responded to the argument that sex between a married couple can strengthen their emotional bond?

The Catholic Church has responded implicitly and partially, in at least one instance where Pope Francis has suggested that married couples could use contraceptives because of exposure to the Zika virus. This does acknowledge the need for sexual intimacy when a good reason - in this case, a particular possibility of foetal defects - exists for not procreating. This is only a very specific case and need not be a precedent for a wider acceptance of contraception, but it shows the Church could in future determine other good reasons for contraception.

I know this does not address your concern for a more general acceptance, by the Church, of contraception, but it is a small step in that direction.

You state:

... if I were to have sex with my wife without the intention to procreate, it would be considered a sin by the Catholic Church.

This is not actually the case. The Catholic Church recognizes that one of the goods of sexual activity is the increase in love and intimacy between the spouses—what it calls the unitive aspect of sex. The Second Vatican Council's pastoral constitution Gaudium et Spes says (section 50):

Marriage to be sure is not instituted solely for procreation; rather, its very nature as an unbreakable compact between persons, and the welfare of the children, both demand that the mutual love of the spouses be embodied in a rightly ordered manner, that it grow and ripen.

Pope Paul VI expanded upon this:

The sexual activity, in which husband and wife are intimately and chastely united with one another, through which human life is transmitted, is, as the recent Council recalled, "noble and worthy." It does not, moreover, cease to be legitimate even when, for reasons independent of their will, it is foreseen to be infertile. For its natural adaptation to the expression and strengthening of the union of husband and wife is not thereby suppressed.

(encyclical letter Humanae Vitae, section 11)

And:

With regard to the biological processes, responsible parenthood means an awareness of, and respect for, their proper functions. In the procreative faculty the human mind discerns biological laws that apply to the human person.

With regard to man's innate drives and emotions, responsible parenthood means that man's reason and will must exert control over them.

With regard to physical, economic, psychological and social conditions, responsible parenthood is exercised by those who prudently and generously decide to have more children, and by those who, for serious reasons and with due respect to moral precepts, decide not to have additional children for either a certain or an indefinite period of time.

(ibid. section 10)

So then, the Church recognizes the this "unitive aspect" of sexual activity as equal in importance with the "procreative aspect" (though there would probably be a reluctance on the part of pastors to reduce it to purely biochemical interpretation). It is for this reason, for example, that the Church is strongly against artificial insemination—it does not believe that procreation should be separated from the strengthening of the bond between husband and wife, or that the woman's uterus be treated simply as a baby-making machine.

On the other hand, to say that the unitive aspect of sex is equal in importance to its procreative aspect is to say that the converse is true as well: that the unitive aspect is never more important than the procreative aspect. The Church believes that marriage of its nature is oriented toward the begetting and raising of children, and this is obviously part of the purpose of sex. To have sex while specifically attempting and planning not to have children is indeed a sin:

The Church ... teaches that each and every marital act must of necessity retain its intrinsic relationship to the procreation of human life. ... An act of mutual love which impairs the capacity to transmit life which God the Creator, through specific laws, has built into it, frustrates His design which constitutes the norm of marriage, and contradicts the will of the Author of life. Hence to use this divine gift while depriving it, even if only partially, of its meaning and purpose, is equally repugnant to the nature of man and of woman, and is consequently in opposition to the plan of God and His holy will.

(Humanae Vitae, sections 11, 13; emphasis added)

Thus the Catholic Church teaches that it is certainly an important aspect of sexual activity that the union and intimacy between husband and wife be strengthened, but also that all sexual activity between the spouses must at least accept the possibility that a child might be conceived.

There are a number of aspects to the O.P.’s question, but it seems to center around the question, “Must the marital act be done for the sake of procreation?” or said in other words, “Must the couple have the intention to have a child whenever they perform the marital act?”

The answer to that question is basically “no,” although the marital act must never be completely dissociated from its procreative purpose. (I will explain below in what way this is so.)

As with other Church teachings that deal with morality, the doctrine on the marital act is based, not so much on Revelation (on what we could only know because God has told it to us) as on what can be known about human nature through reason.

The Church has on many occasions made the case that the procreative purpose of the marital act is one of its essential properties, one that must not be willfully set aside. As Pope Paul VI puts it in his landmark encyclical Humanae vitae,

The Church, nevertheless, in urging men to the observance of the precepts of the natural law, which it interprets by its constant doctrine, teaches that each and every marital act must of necessity retain its intrinsic relationship to the procreation of human life.

This particular doctrine, often expounded by the magisterium of the Church, is based on the inseparable connection, established by God, which man on his own initiative may not break, between the unitive significance and the procreative significance which are both inherent to the marriage act (Nos. 11-12).

It is important to observe, however, that Pope Paul VI does not affirm that every marital act must be for the sake of procreation; merely that it should (as he puts it) “retain its intrinsic relationship” to procreation.

Said in simpler words, couples are not to place deliberately an obstacle to procreation. As the encyclical puts it later on,

Similarly excluded is any action which either before, at the moment of, or after the marital exchange [i.e., the marital act], is specifically intended to prevent procreation—whether as an end or as a means (No. 17; note that the translation on the Vatican website reads “sexual intercourse;” I feel that my translation better captures the meaning of the original Latin coniugale commercium).

There is, however, no problem with engaging in the marital act as a way to bond with one’s spouse. In fact, the marital act is perfectly licit when the couple is infertile, either in the normal course of the woman’s ovulation cycle, or because of some kind of medical problem:

If therefore there are well-grounded reasons for spacing births […], the Church teaches that married people may then take advantage of the natural cycles immanent in the reproductive system and engage in marital intercourse only during those times that are infertile […]. [Such couples] use their married intimacy to express their mutual love and safeguard their fidelity toward one another (No. 20).

Similarly,

The sexual activity, in which husband and wife are intimately and chastely united with one another, through which human life is transmitted, is, as the recent Council recalled, “noble and worthy.” It does not, moreover, cease to be legitimate even when, for reasons independent of their will, it is foreseen to be infertile. (No. 11; the quotation is from Vatican II’s Gaudium et spes, no. 49).

Hence, for example, couples that are infertile for medical reasons may freely engage in the marital act.

It should be noted from the above passage that the Church views the marital act in a very positive light. It is absolutely not, for instance, an “evil” that must be tolerated in order for there to be more children.

In summary: the Church simply argues that it is immoral to place an obstacle deliberately in the way of procreation, when one engages in the marital act. Thus frustrating and essential property of the marital act is what the Church calls contraception.

(It should be noted that it can be licit to delay having children, or even to suspend child-rearing altogether; however, the only licit way to do that is to abstain from the marital act when the woman is fertile. With advances in modern gynecology, this option has become increasingly feasible and accurate; there is, for instance, the Billings method and the Creighton Model.)

Clearly, then, engaging in the marital act for reasons other than procreation—so long as procreation is not deliberately defeated, and in general, the spouses treat each other with love and respect—is not a problem at all.

Hence, the Church is entirely in favor of husband and wife engaging in the marital in order to bond with one another. That idea comes from none other than St. Paul:

Do not deprive one another [i.e., of the marital act], except perhaps by agreement for a limited time, that you may devote yourselves to prayer; but then come together again, so that Satan may not tempt you because of your lack of self-control (1 Cor. 7:5).