No...
You get the implementation you specify. Every time. No exceptions. That implementation does not change because the object is const or not. The code is the code, and it doesn't magically change because you invoked one overload vs. another.
jb4
"So don't pay attention to the approval ratings that say 68% of Americans disapprove of the job this man is doing. I ask you this, does that not also logically mean that 68% approve of the job he's not doing? Think about it. I haven't."
— Stephen Colbert, at the White House Correspondent's Dinner 29Apr06