Does teaching an intro course with a functional language really help level the playing field?
Let me mention, at least, another dimension to this. There are various functional languages and some of them are closer to what your students may have in their backgrounds. A language with dynamic scope and abstract syntax is a very different beast from one with lexical scope and a rich syntax. 

The only functional language that I really worked at was ML and I got quite good at it. But I learned that I really want the concrete syntax that it offers as an aid in my thinking. The underlying concepts are the same, of course, but I'm pretty worthless in Scheme. But then, I didn't learn Emacs from my mother as many schemers seem to have done. 

So, if you want to level the playing field then I will guess that you want something as unlike their previous experience as possible. Say Scheme, rather than Haskell. 

However, some students will pick up the new ideas faster than others no matter what you do, so it is good, in my view, to take advantage of that. 

And of course, if you are going to do something very non-standard, make sure that you have the necessary expertise first. That isn't a situation for staying one chapter ahead in the book as some instructors are forced by circumstances to do.