Nope, you can't (unless you're writing poetry or lyrics or something).
What you could say, but which sounds a bit poetic and stilted, is "Inte heller han talar engelska.". This is specifically the kind of heller which means that there's also another person not speaking English.
On the other hand, "Inte talar han heller engelska." (there's another person) or "Inte talar han engelska heller." (there's another language he doesn't speak) are perfectly fine. Starting with "inte" maybe makes the whole sentence feel a bit stronger.