Yes, presumably such a baptism would be valid. Though not unconditionally. The basic requirements for validity are summarized in three aspects: intent, matter and form. As long as these are present, the sacrament is valid, regardless of the worthiness of the minister, and so the Council of Trent anathematizes anyone who denies that heretics can validly administer baptism. The necessary intent is only “to intend to do what the Church does.” This does not mean that the understanding of the sacrament has to be correct, only that they intend to do that thing that Christ instituted and commanded the Church to do. The proper matter, in this case water, is also presumably present.
Form is a more difficult aspect to maintain. The valid form is, “I baptize you in the name of the Father and of the Son and of the Holy Spirit,” or something very similar." I once was at a Baptist service where they were performing baptisms. Most of these were rather unremarkable: a testimony about their conversion, the words of baptism from the minister, and immersion in the pool up in the baptistry balcony (which I’ve always found an interesting architectural choice). However, there was one girl who was baptized by her father, and he did not use the usual form, but rather, “I baptize you in Jesus’ name. Amen.” According to the teaching of the Church, this would not be invalid, an when I asked my companion about it, she told me that it was unusual and she could see a few people bristle at it. Nevertheless, because of their different beliefs, the girl’s baptism will probably never be redone. So you have a girl who, although she believes baptism is only a symbol, from our perspective thinks she has been baptized, but in reality has not.
That’s just an example to answer your question about validity, but like I said earlier, there is more to a sacrament than just validity. There is a distinction between the validity and liceity of a sacrament. It can be the case that a valid baptism is administered, but that the baptism is illicit (meaning not allowed). In the case of baptism, the ordinary ministers are bishops and priests. Laymen are only allowed to administer baptism in cases of grave necessity. In your case, there is no such necessity. Since you are baptized, you are not bound by canon law, but you are bound by the principles that inform it, part of which I touched on above.
It might also be worth mentioning another aspect of baptism, and that is the distinction between grace and character. Character is the mark of the sacrament that conforms us to Christ and disposes us to the graces of the divine life. This character is “indelible” (think "delete), meaning that it is permanent and cannot be taken away. Character may be called a grace because it is a freely-given gift of God. However, when we speak of grace unqualified, typically we mean what is commonly called sanctifying grace, the grace that cleanses us of sin and makes us pleasing in God’s sight. This is not equivalent with the character nor does one always imply the other.
First is the case of the grace being present without the character. This would be the case in the saints of the Old Testament who, though they lacked the character of the sacrament of baptism not having been instituted yet, still had the grace of God in them. This is also true of the catechumens today who, though they have not received the sacrament of baptism, nevertheless are sanctified by God’s grace through their ardent desire for the sacrament. Baptism of desire does not do away with the need for baptism, nor is it equivalent in effect to the sacrament, but if someone does have baptism by desire, then they will be saved.
On the other hand, it is possible to have the character of baptism and not have the grace. When baptism is administered validly, it always confers the baptismal character. Yet it does not always confer the grace. Think of someone who receives baptism without faith. They might be baptized validly, but without faith it is impossible to please God, as St. Paul says. Someone cannot be in God’s grace and be displeasing to him at the same time. Such a person, though validly baptized, possessing the indelible character of baptism and never to be re-baptized, would nonetheless be in a state of mortal sin. It is possible to have been validly baptized and never be in God’s grace for even an instant of your life.
Regarding these two cases, I know I would rather be in the first case than the second one. In your circumstances, it sounds like you know enough that there is the possibility of grave sin in receiving baptism in the way you are planning to. I can imagine that the most prominent aspect of the Church’s teaching on baptism is its real conferral of grace, and if that were the only thing considered, it would be easy to overlook the other factors. I hope these considerations will be helpful to you to evaluate your situation more clearly.
Let me know if I can elaborate further on anything.
