Via Mark Thoma, a Federal Reserve Bank of San Francisco article says the answer is yes. Their graph above shows how welfare dependency rates and caseloads have declined since the mid-90s "welfare reform" movement that replaced AFDC (Aid to Families with Dependent Children) with TANF (Temporary Aid to Needy Families.)
In addition, states were given mandates to place strict time limits on the welfare rolls, along with incentives and funds to provide welfare recipients with job training and job search assistance to enable them to leave the rolls quickly. In addition, the Earned Income Tax Credit (EITC) provided cash incentives to "make work pay." Under the old AFDC system, many welfare recipients faced an implicit marginal tax rate in excess of 100% if they took a job. Welfare reform and the EITC have changed that system.
Since Congress overhauled the U.S. welfare system in 1996, single mothers between 18 and 24 have reduced welfare dependency, increased workforce participation, and registered gains in household income. The group's growing attachment to the labor force means they may be better positioned to take advantage of unemployment insurance during the current recession.
The entire article is very much worth reading: Did Welfare Reform Work for Everyone? A Look at Young Single Mothers.