If you take it in the context within which it was written, it could not be referring to America or the RC church. The angel who announces that 'she has fallen' (Rev 18:2-4) is speaking to John in the 1st century and using the aorist tense, as if this is something that has already happened and encouraging "my people" to get out of her before her plagues arrive.. The USA and Christian institutions had not yet come into existence at that point in time. Isaiah chapter 2 better fits the situation described in Rev 18:2-4. According to NT writers, the "last days" corresponds with the whole of the Christian era starting with Jesus' first advent. (Heb 1:1-2)
On the idea that it might picture the USA, there was a fictional book that took it that way, called Alas, Babylon (here).