That would be a qualified yes. As an example, the Gates Foundation has given a bit over a billion dollars to the Global Fund to fight AIDS, Malaria, and Tuberculosis. Those three diseases are among the biggest causes of (relatively) easily preventable deaths. In terms of vaccines, research is being done to develop a vaccine for malaria (which causes about 1% of global deaths), but vaccination may not prove to be the most effective means of eradicating the disease. Things like antimalarial drugs and mosquito netting may be more cost-effective, and so malaria rates have dropped dramatically despite there not being a vaccine. There is a vaccine for Tuberculosis, but it's definitely not cost-effective. AIDS is no longer a death sentence, though no vaccine exists. So in terms of Malaria and AIDS, the foundation has been reasonably successful (tuberculosis is proving to be a rather more difficult problem).
So the Gates Foundation has contributed to improvements in health, though again, the contribution is fairly limited (as one would expect when talking about a fund with only $30 billion, which is a huge amount of money for an individual but pretty much insignificant on a global scale).
Correction: no FDA approved HIV vaccine exists, yet. However, HIV vaccines do exist and are in, or will soon be in, clinical trials. That doesn't necessarily mean that they will be proven to be safe and effective, but it's not unreasonable to imagine that one of the vaccines in the pipeline will prove to be.
So the Gates Foundation has contributed to improvements in health, though again, the contribution is fairly limited (as one would expect when talking about a fund with only $30 billion, which is a huge amount of money for an individual but pretty much insignificant on a global scale).