Does more inequality increase growth? Theoretically, the relationship is ambiguous. Let us take to effects to illustrate this by focussing on the incomes of the richest. If these increase, the aggregate savings rate gets higher as the richest have typically a below average marginal propensity to consume. The higher savings rate leads to more capital accumulation, and thus higher wages for everyone and higher GDP. However, the same rise in top incomes puts more pressure on increasing redistribution, and we know that more taxation leads to more inefficiencies, say through diversion of resources into tax avoidance and through lower incentives to work. Which effects dominates, and there are others, is an empirical matter.
The literature is largely inconclusive on this. Cross-country regressions are particularly ill-suited for this, because the level of inequality in an economy can have many reasons that maybe correlated is some way with growth. Time-series studies are also problematic because of the possibility of a Kuzents curve: As an economy develops, on can expect inequality to rise and then fall. And in both cases, the measurement of inequality is always problematic.
Dan Andrews, Christopher Jencks and Andrew Leigh claim to do this better by focussing on just the top incomes (easier to measure than, say, a Gini coefficient) and by exploiting the pannel feature of their data. They conclude that a rise in top incomes, at least after 1960, has a positive impact on the growth rates in 12 OECD countries. Specifically, a 1% increase in the top income share leads to a 0.12% increase in the growth rate. If this income change is permanent, the growth rate change is permanent as well. On theoretical grounds, I find this hard to believe and that may be a result of the rather short period they are looking at (40 years in 5 year intervals). Imagine what this means in the context of a Solow growth model: The permanent shock means that the aggregate savings rate is higher. That leads to a higher capital level, but not a higher steady state growth rate. It looks like there is still a lot of work left in this literature.