Are salaries for government workers part of GDP?

Yes, salaries for government workers are definitely part of GDP.
First, GDP has a few components. These are:
1) Business investments that lead to the creation of new products.
2) Consumer expenditures, where consumer spending is 70% of GDP.
3) Imports and exports.
4) Government spending, which consists of mandatory expenditures and discretionary expenditures. Mandatory spending includes Social Security, Medicare, unemployment payments, federal worker retirement benefits, and Medicaid payments. Mandatory spending for 2019 will be upwards of $2.5 trillion for the year. Our two largest mandatory spending programs are Social Security and Medicare, which makes up about 62% of government spending. These programs dwarf the military budget.
Meanwhile, discretionary spending includes government worker pay, military salaries, and government investments in equipment and software.
For discretionary spending, about 15-17% are allocated for government worker salaries. Examples of government worker salaries are Department of Defense civilian pay and Pentagon salaries and benefits.
https://www.investopedia.com/ask/answers/082415/are-social-security-payments-included-us-gdp-calculation.asp

https://www.nationalpriorities.org/budget-basics/federal-budget-101/spending/

https://www.thebalance.com/components-of-gdp-explanation-formula-and-chart-3306015

The answer to your question is yes, the salaries for government workers are considered "government expenditures" in GDP. This is true whether or not the hired government worker successfully contributes to the economy.
Contrast this with private sector hiring. In the private sector, when an employee is hired, there is no inherent addition to the GDP. GDP is only affected by the private sector when product is created.
It is occasionally suggested by some who wish to stimulate GDP that the government hire en masse. While increased governmental hiring has the potential to add value to the market, the actual act of hiring does not inherently create anything besides salary costs. Because of the way we calculate gross domestic product, this action would add to the GDP and on paper appear to be an economic benefit. It should be remembered, however, that this action may not positively affect profits and therefore may not be as beneficial as it appears.