I think it does. But first, perhaps, a word on public social spending. What is this? It’s government support for those in need. This can be financial or other types of support. It can be cash benefits such as unemployment checks, tax advantages (e.g. to poor families with children), or “in-kind” goods and services such as free wheelchairs for the disabled. “Public” means that the government provides this support. (There’s also private social spending: e.g. companies can voluntarily pay their employees an additional amount for child support or old age pension).
The graph below shows that there is a correlation between relatively high levels of public social spending (measured as a percentage of total N.N.I.) and relatively low levels of income inequality (measured with the Gini-coefficient):
(source, click on the image to enlarge)
So we can assume that helping the needy does indeed push their income upward, and reduces inequality. This of course corresponds to a widely shared intuition about the importance of a social safety net and income distribution.