I think you're asking if SSA is still a functional language in the presence of mutation of memory. Both Scheme and ML (of Standard ML and OCaml fame, not machine learning) allow mutation, so mutation doesn't seem to disqualify a language from being functional.
This naturally leads to the question "what is a functional language?" I've written my thoughts on what FP is at [1]. I argue that FP is about local reasoning and composition. The former is most relevant here: local reasoning means it's easy to reason about code. This is exactly why SSA is used in compiler: it makes it easy for the compiler to reason about code and therefore which optimizations are valid. This is the same argument given in these comments: https://news.ycombinator.com/item?id=45674568 and https://news.ycombinator.com/item?id=45678483
This naturally leads to the question "what is a functional language?" I've written my thoughts on what FP is at [1]. I argue that FP is about local reasoning and composition. The former is most relevant here: local reasoning means it's easy to reason about code. This is exactly why SSA is used in compiler: it makes it easy for the compiler to reason about code and therefore which optimizations are valid. This is the same argument given in these comments: https://news.ycombinator.com/item?id=45674568 and https://news.ycombinator.com/item?id=45678483
[1]: https://noelwelsh.com/posts/what-and-why-fp/