I think ironing the binding in half is not a good idea, because of the fact that the outer edge is longer than the inner (described above) when it wraps around. However, ironing the binding toward the other side after it's been sewn to the back or front really makes it very neat. Now, if you're concerned that the binding separates as you're working if you don't iron it in half, you can put a thin stream of Elmer's school glue near the edge of the wrong side and press the edges together so they'll stay while you're sewing, but still don't press the fold because it will lie better if it's not pressed first.
I don't know how clear all of that was--it's hard to describe.