How to add a class to comment submit button?

There is easier way to achieve your idea. But , to be true, I cant easily understand what you need?

1) If you need just to target styling of that button, then no need to add any class. Target it using parent:

p.form-submit input#submit{  
    desired options here
}

2) Maybe you have error in that code. Instead, you should use just button:

....
....
$button ='<button class="btn waves-effect waves-light" type="submit">Post Comment<i class="material-icons right">send</i>';