It is well known, as well as found in sefarim, that checking tefillin and mezuzos to find mistakes can bring great yeshuos. Why should shaatnez be any different?The tefillin and mezuzah stories are already, IMHO, a bit too much. But this is yet another example of the segulah-ization of Judaism, taking things which are mitzvos -- aseh or lo saaseh -- and performing it not because it is mitzvas haBorei but because it is an easy magic ritual to get what you want. And here, it is not even with any quasi-valid source, but rather a "logical" extension.
Indeed, why should checking that your tzitzis are intact be any different?
Why should checking your food for bugs be any different?
Why should checking the lungs for sirchos be any different?
Why should a woman performing a bedika be any difference? Indeed, for this one, we even have a statement of Chazal we may misrepresent as promising a segulah -- כל היד המרבה לבדוק בנשים משובחת.
Why should bedikas chametz be any different?
(And perhaps segulahs already exist for these.)