I think that Carnegie's work seeks to solve these problems. If one were Carnegie or any of the other industrialists, I would think that the ideas that he espouses probably does seek to solve any potential problems posed by the Social Darwinist philosophy. One has to remember that many industrialists were not really searching for philosophies to justify their actions, for they simply did what they could to maximize their profit. At the time period, if anyone were voicing problems with Social Darwinism, most of these individuals were already being silenced by the timbre of the time which was pro- industrialism and favoring those who own the economic means of production. Over time, we have acknowledged and realized that the Industrialists like Carnegie, Morgan, and Rockefeller were very instrumental in establishing our modern notion of industry and wealth. Yet, we also are aware that within the action of immense creation was also a sphere of intense destructive elements, especially to the ideas of workers' rights and fair compensation.
That's a tough question... I suppose I would probably say no. Here's why:
The problems that you ascribe to Social Darwinism are, presumably, the poverty and poor working conditions experienced by working class people during the Gilded Age.
The Gospel of Wealth held, as its main concept, the idea that the people who got rich during this time should use their money for the benefit of the people who didn't. However, the ways in which the used their money (the charities to which they gave) were not usually designed to help the working people in the short term.
Just two examples are all the money that Carnegie spent on public libraries and the money Rockefeller spent to create my alma mater, the University of Chicago.
Both of these could be said to help people in the long term, but they didn't give the working poor much immediate help.