If you are causing the reference count to be modified, yes there is some overhead. If you pass the shared_ptr<> by reference then you have extra indirection accessing the object itself.
... if I am just passing the pointer around and calling .get() as a function parameters, is there much overhead in that?
However, I would argue that unless the function you are passing the object to is allowed to assert ownership, do not pass a shared_ptr just for semantic reasons. Better to pass a const reference (if null values are not expected), or a raw pointer (if your coding convention supports the idea that a raw pointer passed to a function has no special ownership semantics).