The positive effects of a relationship between these things would be that more scientific research would be funded and carried out. This could lead to better understandings of the world and to the creation of technology that would help us live better lives. A good example of this is the National Science Foundation, which helps fund research that can end up benefitting all of us.
But this relationship can be bad as well. This is particularly true when science gets taken over and abused for partisan reasons. This sort of dynamic can be seen most clearly in the US on the issue of global climate change. On this issue, science has become a battlefield and people use or misuse science to support their side of the issue, regardless of what claims can legitimately be supported by scientific research.
So, there can be good and bad aspects to this relationship. It can lead to an increase in knowledge and in beneficial technology, but it can also lead to the misuse of science for political reasons.