I can't quite tell if we're focused only on whether the FED rate can be used for leisure, or whether the question is whether the gov't rate can be used for leisure as well as for work. If the latter, then:

From an LA Hilton property: "Government Per Diem Rates are offered throughout the year* – for business and leisure travel."

To be sure, that is a particular property. But it merely makes explicit that the government rate can be used by government employees for business or leisure.

See, for example, the general invitation from the Hilton website:

"Government & Military

The most recognized name in the industry, Hilton Hotels & Resorts stands as the stylish, forward thinking global leader of hospitality. With more than 540 hotels and resorts in 76 countries across six continents, Hilton welcomes guests in more countries than any other full service hotel brand. If you are a state, federal or United States military employee, you can enjoy great savings with special government and military rates at participating Hilton Hotels & Resorts."

Note that the invitation to government employees is that "you can enjoy great savings." The implication of this seems clear to me: After all, when on government business, the unit one works for pays for the room; the government enjoys the savings, not the employee. But when on leisure travel, the employee, "you," enjoys the savings - and is welcomed to it by Hilton and other HH chains.

I surmise that the purpose of the discount is to attract government employees for both work and leisure. I expect because government employee salaries tend to be lower than many other travelers, but they travel as much or more than other work groups (e.g., summer vacations for public school teachers).

The property will state it if the gov't rate is limited to work travel - and then I seem to recall usually requires travel orders rather than merely the presentation of government ID. I see the limitation only rarely.