In the tavern scene where Archie's disguise is blown through his English hand gesture, he is initially questioned by Cprl Willhelm about his unusual accent. Can the German visitors to this site confirm if his accent did sound iffy, and did Stiglitz and the other chaps accents match to where Major Hellstrom guessed?
I, being a German and having heard a wide variety of different German dialects, can confirm to you that his accent was indeed a bit strange. And while Michael Fassbender didn't have too strong an accent, it was IMHO still identifiable as slightly English-based and thus was likely to arouse the suspicion from the Germans in that bar.
Yet the accent wasn't completely weird, given that there might still be hidden places where people speak accents I haven't heard yet, like at the Piz Palü. So I would say that Cpl. Wilhelm would probably not have spoken about it to a higher ranking officer, hadn't he been as drunk as he was, and maybe asked him out of mere curiosity rather than actual suspicion. But they didn't plan to stumble across such a highly suspicious security officer as Maj. Hellstrom, who had all the reasons to request some clarification from Hicox.
But I also have to say that I don't have as good an ear as Maj. Hellstrom and wouldn't really have been able to classify the other two German Basterds according to their home towns as easily as he did, since they spoke pretty clear High German. So that part was maybe a bit exaggerated (or he had really just far better trained ears than I have). Yet looking at the two actors, they were indeed born or grew up at or near the places attributed to their roles by Maj. Hellstrom, so it is pretty reasonable to assume that he was right in his assumption.