Yes, I would think they would want to hush this up and make it go away quietly. Hastert's predilections, while not exactly an open secret in D.C., were rumored for years. There's a character clearly based on Hastert in Sibel Edmund's "The Lone Gladio", and let's just say her version of the character's activities in the roman à clef novel are sickening. I don't think the details will ever come out because some government involvement seems likely. But at least he's going to jail, which is better than nothing:

Former House speaker J. Dennis Hastert has agreed to a tentative deal with prosecutors to resolve charges that he violated banking laws to cover up hush money payments related to long-buried misdeeds, his lawyer told a federal judge Thursday.

The deal could mean that details of those past misdeeds will never be aired in open court.

Several people familiar with the case have said that the payoffs, to total $3.5 million, were to cover up allegations of sexual misconduct dating to Hastert's days as a teacher and wrestling coach in Illinois.

[...] Those two counts each carry maximum penalties of up to five years in prison and $250,000 in fines. Under a plea deal, Hastert can expect a much more lenient sentence.