The scathing and salacious federal indictment against Hunter Biden on tax evasion charges has provided a boost to House Republicans at a critical time in their impeachment inquiry against President Biden, spotlighting the kind of wrongdoing by his son that they have repeatedly tried and failed to connect to the president himself.

Republicans immediately hailed the indictment — with descriptions of payments to “various women,” stays at deluxe hotels, a membership at a “sex club” and at least one Lamborghini rental written off as business expenses in a “scheme” to dodge a $1 million tax bill — as a validation of their inquiry. The charges, they said, would never have been brought without the testimony of two I.R.S. agents who have become congressional whistle-blowers and blew up a “sweetheart” plea deal between Hunter Biden and prosecutors.

Yet in the most critical respect, the indictment is far from helpful to the Republicans: It never mentions President Biden, not even indirectly, and provides no evidence linking the misdeeds of the son to the father.

Republicans have a steep challenge to build a bridge from Hunter Biden’s vices to their allegations that his father has committed high crimes and misdemeanors, and to show that their impeachment inquiry is anything other than retribution for the impeachments and indictments of former President Donald J. Trump.

Still, for the small group of mainstream House Republicans who once were queasy about diving into what appeared to be an evidence-free, politics-driven impeachment inquiry, the latest indictment of Hunter Biden provides a measure of political cover at an important moment.

Buoyed by the charges, House Republicans intend to push ahead next week with their plans for both a floor vote to authorize the impeachment inquiry and a demand that Hunter Biden testify behind closed doors on Dec. 13 — promising contempt of Congress charges if he continues to refuse. Aides working on the investigation said they expected no changes to their strategy.