In general, I would say "no, the Church would not approve" simply because of the confusion that resulted from this service. A pertinent document on this topic (as well as many others) has a rather cumbersome, yet descriptive and accurate, title: Instruction On Certain Questions Regarding the Collaboration of the Non-Ordained Faithful in the Sacred Ministry of Priest.
In the Church, as in civil government, the power of governance is divided into legislative, executive, and judicial powers (canon 136.1). Diocesan bishops possess all three powers and only Bishops can be legislators, unless the Supreme authority in the Church has given someone else this power (canon 135.2). When I look at a document, I first want to know what authority the document has. To come to a conclusion, I ask questions such as "who wrote this? A legislator? An executive? Is it binding as law? Is it applying the law and serving it? Is it an exhortation?" When I look at this On Certain Questions document the first word I see is "Instruction." That should tell me it is not legislative and therefore it should only be applying law that already exists. The Code of Canon Law makes this clear: legislation (canon 29) is of greater "weight" than Executive Decrees (canons 31-33) or Instructions (canon 34) because the last two must serve legislation.
Normally, then, an Instruction is a document that is executive in nature. It describes how laws are to be enforced by those with this duty. An Instruction is not "law." It serves the law that already exists. If any part of an Instruction contradicts the law, that part is without effect. That's the standard purpose and function of Instructions in the Church. The typical lay person will not have much exposure to Instructions since, as noted, they are directed toward those who have executive authority in the Church and we lay people don't have it. Unfortunately, the most commonly encountered "Instruction" is not an Instruction at all--the "General Instruction of the Roman Missal." This document has legislative force and is actually called the "Institutio." And, the point I am getting at in all this is that this Instruction On Certain Questions is not a normal Instruction. Here's why.
It was prepared and approved by six Congregations and two Pontifical Councils at the Holy See. This is unique but would not necessarily make the document any more authoritative than if only one Congregation had composed it. The deciding factors are these: it was approved in forma specifica by Pope John Paul II, meaning the Pope has made this document his own. It is not really a document of any Congregation: it is a papal document. Second, it was "promulgated" as laws are, not "published" as Instructions would be (see canon 7 and canon 34.1). Finally, it contained a broad, revoking formula: "All particular laws, customs and faculties conceded by the Holy See ad experimentum or other ecclesiastical authorities which are contrary to the foregoing norms are hereby revoked." An ordinary Instruction cannot do this.
What we have here in this document, then, is legislation of the highest order--from the Pope. The purpose of the Instruction is to "provide a clear, authoritative response to the many pressing requests which have come to our Dicasteries from Bishops, Priests and Laity seeking clarification in the light of specific cases of new forms of 'pastoral activity' of the non-ordained on both parochial and diocesan levels." Sometimes, lay people can carry out tasks that confuse their proper role with that of priests, and vice versa: proper "collaboration" must maintain essential distinctions between the ordained and lay faithful.
What, then, does it have to say about the question of lay people anointing others? In Article 9, we read:
§ 1. ... The non-ordained faithful particularly assist the sick by being with them in difficult moments, encouraging them to receive the Sacraments of Penance and the Anointing of the Sick, by helping them to have the disposition to make a good individual confession as well as to prepare them to receive the Anointing of the Sick. In using sacramentals, the non-ordained faithful should ensure that these are in no way regarded as sacraments whose administration is proper and exclusive to the Bishop and to the priest. Since they are not priests, in no instance may the non-ordained perform anointings either with the Oil of the Sick or any other oil.
§ 2. ... It must also be affirmed that the reservation of the ministry of Anointing to the priest is related to the connection of this sacrament to the forgiveness of sin and the worthy reception of the Holy Eucharist. No other person may act as ordinary or extraordinary minister of the sacrament since such constitutes simulation of the sacrament. (105)Just to make things harder for us, this passage includes a faulty translation. The official text concludes paragraph 1 by saying "in no instance may the non-ordained perform anointings either with the Oil of the Sick or any other non-blessed oil." For some time, I didn't know the English was deficient and I have tried to make sense of this total prohibition on the laity performing anointings of any sort. In the preceding sentence, the laity were told that their use of sacramentals has to be kept distinct from the Sacrament of the Anointing of the Sick. Well, if they can't use any oils in anointing, what sacramentals that could be regarded as the Anointing of the Sick are left? Besides, why couldn't a mother, for example, use some oil from St. Joseph's Oratory and anoint her injured child's wounds and ask for the intercession of St. Joseph? The total ban seemed pretty draconian so I tried to weasel my way out of it, using the context of the paragraph. Well, it's not a total ban. It is a ban on using non-blessed oil. That makes a lot more sense: don't just go to the cupboard, get some Great Value® vegetable oil, put it on someone, and think it is a sacramental. It's not. It's just some cheap, Wal-Mart oil.
Getting back, finally, to the scenario presented in the beginning of this post, I'd repeat that if the participants were left in wonderment and confusion as to what was going on here, it was inappropriate. The anointing with oil was done on the forehead and hands, just like the Sacrament. That, in itself, makes me think it was improper since it looks like the Sacrament. Were any words said with the anointing? I don't know. If there were no words spoken, I wouldn't say that this ceremony was simulating the Sacrament. If the words of the Sacrament were used (Forehead: "Through this holy anointing may the Lord in his love and mercy help you with the grace of the Holy Spirit." Hands: "May the Lord who frees you from sin save you and raise you up."), however, that would be more problematic and would cross another line.