In Catholic doctrine, “membership” has a specific definition–it is full incorporation into the Church through baptism, profession of faith, and hierarchical communion.
That doesn’t mean there aren’t other relationships one can have with the Church or even means of belonging that can be salvific. Catechumens, for example, are said to belong to the Church by their faith and intention, but they are not yet members since they have not been baptized. A person such as you describe, if motivated by faith and charity, could indeed belong to the Church in a similar way. Some old Catechisms call this belonging to the “soul of the Church” since it is a spiritual link.
That being said, non-Catholic communities cannot be said to be the Church of Christ–that is only the Catholic Church. But again, their members can have a relationship with the Church based on their faith and baptism and, if otherwise properly disposed, may even belong in a salvific way–but they are not “members” (properly so-called) of the one Church.