Although I read the book when it first came out, I have basically zero memory of it, so I don't recall if FTL communication is essential to the story. However, having just watched the first season of the Netflix season, I explicitly noticed that even though it mentions use of FTL communication, the story absolutely doesn't need it at any time. There's a local representative of the distant folk who is clearly trusted to make decisions, and could represent the distant folk for all communication purposes.
When Evans speaks with the San Ti/Trisolarians, he is talking to them via one of a pair of sophons - quantum entangled protons.
Whether this changes their chance of success is certainly debatable, but it definitely changes their behavior.
(0) note that AFAIR from reading book 1 just about a month ago, this is series-canon, not book-canon.