I have considered that possibility, and it's a legitimate, though wildly overblown concern. Sure that probably happens to some extent. I have a very good friend who manages an SRO in Portland who constantly complains to me about this very thing. To the extent that it's an issue, it's better addressed by restructuring certain aspects of the welfare system than by destroying it completely (e.g. by providing financial incentives to either get an education or actively search for a job, or acquire job-related skills, etc). It's also largely irrelevant to things like educational policy (which I consider far more important than welfare as such). Additionally, there are plenty of ways to stimulate economic growth and benefit blue collar America that don't involve directly giving money to people who aren't doing anything productive. Government construction programs for instance.
Definitively? No. I'm not an economist, and my understanding of economic thinking suggests that economists tend to differ wildly on this issue as well. But I think it's equally impossible to reach any solid conclusions to the contrary either. Having said that, it's pretty clear that the US experienced a period of unprecedented growth during the 50s and 60s, and while this might not have been because the wealthiest, most successful Americans were taxed at rates far higher than we see now, it clearly happened even though the wealthiest Americans were taxed at extremely high rates (again, compared to now). It's equally clear that in the wake of conservative (and sometimes neo-liberal) deregulation of the financial sector (which has been happening for the bulk of my lifetime) and in the wake of significant reductions in taxes on the wealthy, our economy has gotten weaker and our schools have gotten much worse.