If anything the type system improves the run time speed, because the static analysis enables better code generation.
But I think what OP meant was more about the "functional programming" side of things than the "HM-typed" side of things. Naively, anyway, you might think that "the FP-style" of avoiding mutation and preferring recursion would require lots of garbage and high-latency garbage collection, copying, function call overhead...of course, that's not the whole story, but having Jane Street to point to as a crushing counter-example is nice.