I was told by my home advisor and I think I read somewhere that if you do away early enough to have reasonable time to get a letter and you DONT get one, it would look odd - like you were trying to hide something. The other thing to keep in mind about away rotations is where you are doing it. The advice I was given was to either do an away at some place you really want to go - or if you have no preferences, do an away at one of the "really strong programs" (whatever your definition of those are) - ie one with a national reputation. I think the latter is especially true if you are coming from a place with NO academic EM department/no residency program of its own.
When I arrived for my away rotation, I talked to the medical student coordinator (administrative type - not physician) about who she thought would be able to write a strong letter. She juggled my schedule a tad and made sure that I had a few shifts with that person. Then, I worked my ass off during those shifts and other shifts for the first 2 weeks of the rotation and made sure that I was getting positive feedback.
Then, I made a separate appointment during office hours to go and talk to that attending who I had those shifts with and had developed a good relationship with (if you can really develop a relationship in 2-3 shifts). I asked his advice about whether I should obtain a letter from my month there. This was kind of a way to test the waters before having to officially ask for a letter. He said "Of course, and I would be happy to write it if you would like". So I really never asked for it directly. Then I immediately supplied him with my completed ERAS application, transcript, personal statement, CV and ERAS waiver cover sheet. (Had them in my bag with me at the time).
Finally, since I had made good friends with the student coordinator, I was able to "check" on the strength of my letter on the side in casual conversation (she was this person's secretary also and typed the letter for him).
Now this is the way I did it. Doesn't mean it is the only way or the correct way.
Good luck!