It seems so, according to the job market paper from Mario Alloza (pdf):
The results obtained suggest that higher marginal tax rates reduce income mobility. Particularly, I find that an increase of one percentage point in the marginal rate is associated with declines of about 0.5-1.3% in the probability of changing deciles of income. A decrease of 7 percentage points in the marginal tax rate (slightly smaller than a standard deviation of non-zero changes in the rates) can account for about a tenth of the average income mobility in a year. The effect of taxes on mobility arises in specifications that consider income distributions both before and after taxes and transfers, suggesting that the impact of taxation on mobility goes beyond redistribution effects. The economic mechanism that induces this impact seems to be related to the labour market incentives created by changes in the tax schedule.
Interestingly, these effects are especially pronounced toward the bottom of the income distribution. If the implied labor supply response seems too high to you, then read some of the recent papers by Karel Mertens. The idea that taxes matter is making a comeback in economics, though I am not sure you would get that impression from most of the economics blogosphere.
Do note the mobility results cover taxes only, and not how the money is spent.
For the pointer I thank Peter Isztin.