No, it doesn't improve speed significantly, or anything at all. On the contrary, by using the ref keyword you are adding another level of indirection that only can make the code slower.
Parameters are normally passed by value, which means that they are copied. For simple values like int, it simply means that a copy of the value is placed on the stack.
For reference types like a string it means that a copy of the reference is placed on the stack. So, it doesn't mean that the entire object is copied, it's just the reference to the object that is copied.
You should generally not use the ref or out keywords, unless there is a special reason to do so.