@Writeorwrong
They will find out one of a few different ways but these two are the most likely.
A: Your son gets accepted, opens up to his Rebbe about problems at home, the Rebbe fearing for the neshamos of the other talmidim brings this issue to the attention of the hanhala at once, because clearly this boy is influenced by his older sibling and is a ticking time bomb.
B: Someone from your neighboorhood runs into someone who has a child in said Yeshiva and then through the usual frum lashon harah l’toeles grapevine, word gets out and pretty soon not only painted with the stigma of an otd sibling, he is now a “liar” too.
Mi K’amcha Yisroel.