There are a few variables not listed... are you MD, DO, US IMG? Most seem to assume MD, and since you list about your home institute, it most likely is true. Second, are your scores/stats up there, middle of the road, or low? Third, how many students from your class are going into surgery, and how many want to stay at your home institution? Last year, we had like 20 wanting to go into Gen Surg, we matched 3 at our home institution, but I know of several who matched at places lower on their rank list than the home institution. The 3 of us that did match, one common demoninator was multiple surgical rotations within our program and those with important members of the faculty (Myself was well known and liked by PD, Chairman, and chair of surg onc, as well as the residents who I've been told went to bat for me). Another student was very well known by the trauma team which has a lot of pull with our selections, and the last was also very well liked by the PD, known to chairman (but unsure of his perception of her). So don't just assume you will match at home institution. It seems your schools academic year is very late if you are just setting up 4th year schedule in mid july, unless you are slightly off schedule. Our 4th year starts June 1, and for June, July, August, September, and October I did surgical rotations (Community college affiliated with my school, Surg Onc, Chairman's rotation[AI], Away, and PD's rotation). You don't have to go that rediculas, but you need to assure yourself 3 letters of recommendation from surgeons, and you probably can't necessarily bank of 3 from an AI... 2 wouldn't be unheard of (i only got 1, but could have gotten a second if I needed it). It also doesn't hurt to let your intentions of staying fairly well known so residents can help you out, give you advice, and in the end, if they like you, lobby for you.
Now, another, unrelated to getting in reason pro doing an away is this: If all you ever know or see is your home institution, how do you know if surgery or that school is where you want to be for residency? Every place, and everyone does things slightly different. Teams are organized differently, computer systems, services, operative experience, academics/didactics. And believe me, you don't get to see much of anything during your interview, especially nothing that really matters for how life will be as a resident. By the time I made my rank list, I had seen at least a day around the surgical residents in 5 programs (home program, 3rd year rotation at an affiliated institution, 4th year rotation at community hospital that rotated residents through it, my away, and a second look) and there are similarities and there are vast differences. I was much more comfortable staying at my home institution (a "mid" tiered academic institution with inner city trauma experience) over going to a bigger name (and was actively recruited by 2 places appearing on the honor roll of top hospitals in the country, one because of my away, the other because of my letters/application).
So bottom line: Don't have to do aways, but i'd recommend doing them for yourself (so doing late october/november and not getting a letter is fine, you still will make an impression on them and it will make an impression upon you). You don't need 5 surgical rotations at your home institution, but if you truely want to go there, you would probably benefit from more than just 1, and for letter receiving purposes, you probably need more than 1 anyway. Let your intentions known (but not too loudly) and get in good with the residents at your home program, cause some places they have more swing than you'd think (especially chief/administrative chief residents)