Short answer. No. Article 818 of the Civil Code prohibits two or more persons from making a will jointly or in the same instrument, whether it is for their reciprocal benefit or for the benefit of a third person — so the fact that the joint will would benefit someone else entirely does not create an exception.
What the law says
Two or more persons cannot make a will jointly, or in the same instrument, either for their reciprocal benefit or for the benefit of a third person.
Civil Code, Article 818 — Joint Wills Are Prohibited. Read the full provision →
The prohibition covers third-person beneficiaries too
Article 818 states plainly that two or more persons cannot make a will jointly, or in the same instrument, either for their reciprocal benefit or for the benefit of a third person. The article does not limit the prohibition to wills meant to benefit the two testators themselves — it expressly extends the same bar to a joint will meant to benefit someone else entirely, which is exactly the scenario in your question.
Two separate forms the prohibition targets
The article bars joint wills in two related ways: making a will jointly, and making it in the same instrument. Even if the two people intend entirely separate dispositions, putting both wills into one physical document is itself what the article prohibits — the problem is the joint or single-instrument form, not only the possibility that the dispositions might somehow be treated as reciprocal.
Why the reciprocal-benefit and third-person cases are treated alike
By naming both reciprocal benefit and third-person benefit as covered situations, the article makes clear that the specific purpose of the joint will does not change the outcome. Whether two people are leaving property to each other, or are jointly leaving property to somebody else altogether, the same instrument and joint-execution problems the article is concerned with are present either way, so both situations fall under the same prohibition. That is also why consent is beside the point: the prohibition binds the testators even where both of them, and the intended beneficiary, are entirely willing.
What this article does not resolve
Article 818 establishes that a joint will of this kind is not permitted, but it does not itself describe what happens to two people's actual testamentary wishes once the joint format is off the table, or how each of them should instead go about expressing an intent to benefit the same third person. Those questions are addressed by other rules on how a valid individual will must be executed. What each person can do is make an individual will in a separate instrument of his or her own, naming that same beneficiary.