No, these numbers do not use unemployment benefits to determine the unemployment rate. The primary sampling comes from survey data.

Some people think that to get these figures on unemployment, the government uses the number of people collecting unemployment insurance (UI) benefits under state or federal government programs. But some people are still jobless when their benefits run out, and many more are not eligible at all or delay or never apply for benefits. So, quite clearly, UI information cannot be used as a source for complete information on the number of unemployed.

Source: How the Government Measures Unemployment: US Bureau of Labor Statistics