Essentially, without perfect pitch, could someone learn a language that requires you to have the pitch perfect.
I think no one knows this answer for the general case because no one knows whether all people can learn perfect pitch. I don't think we know what causes this "talent" to say what are its limitations. There is evidence that some people can.
A 2015 study found that some adults can acquire perfect pitch for months. Presumably the initial study's methods are theoretically improvable and repeatable. If you can accept the sci-fi speculation that warp drive is plausible with effort, then surely you can accept the lesser speculation that perfect pitch is plausible with effort. If you want to make the solution more colorful, then maybe write that medically inducing some kind of synesthesia is easier than teaching conscious, full-speed perfect pitch ;)