So far, they've conveniently avoided anyone she knows seeing her in costume. Naru almost did, but fell unconscious first. Umino almost did, but was dazed from brainwashing.Pretty much the only time it was even suggested someone could see through the "disguise", I believe.
The first episode cut from the dub was Episode 02 : you know, the one where Umino flips up Ms. Haruna's skirt and acts like a delinquant.According to Wikipedia, it's the second one cut, and they don't list reasons. But I suspect you're right.