I certainly know a few people, mostly foreign-trained, who got a leg-up in the application process by doing a visiting rotation. It helps you to some degree to put a face with your name, see how you fit in, and helps to separate you from the mountains of FMG applications and CVs many programs receive. You have to do it right, though. I had plenty of "visitors" rotating on my service from other countries who didn't get insured, and so couldn't touch patients. They couldn't do anything to help, couldn't show their skills, and mostly just got in the way. Don't be that guy/girl.
As far as I know, my program never had acting internships, so I'm not sure about that. Our visiting elective students take call and carry patients on the ward, so I guess I'm not even sure what the difference is.
Finally, I agree that most neuro residents never did an away elective, at least not in my experience. I certainly never did, and I didn't feel like it hindered my choices in any way. If you want to do an away elective, do it for you to get a better feel for a program or a new city. You don't really need to do it for them.