In Dignitas Personae section 18 and 19 the Catholic Church asserts the personhood of cryopreserved embryos and, although it objects to IVF and other techniques for several other reasons, a major objection is that many cryopreserved embryos are not revived. It specifically objects to cryopreservation carrying the risk of death for human embryos, implying that they are either living or at least not-dead, and suggests the possibility of "prenatal adoption", and also objects to any medical use or destruction of the embryos.

So, in a narrow sense, they already believe that frozen people are alive enough to be worth keeping frozen or reviving.