I think that aways are a great way to get ahead. Do one at a reach school, because you basically have nothing to lose. If you show up and look like a doofus for 4 straight weeks, well, at least you weren't going to get an interview in the first place. In my humble opinion, it seems as though programs really do take aways into account when sending interview invitations, even though they might claim otherwise. You don't necessarily have to be a superstar on the rotation, just show up on time and work hard (as a student, you can't really impress anybody in anesthesia anyway. There is nothing that you can do that a SRNA 2 weeks into training can't do. Trust me.) An away mostly lets the program know that you have legitimate interest, as opposed to a "what the hell" tack-on application, of which there are hundreds. Keep in mind that program directors have to sift through hundreds of applications, many of which look exactly the same. If you have 2 identical applications on your desk, but one person rotated at your institution for a month, who are you giving the interview to?
I'm no genius, but I did an away at a big name institution that seemed like a pretty big reach at the time of the rotation. I received an interview invitation relatively promptly. Go for it.