Actually, it has a very direct role in our salvation. Good behavior doesn’t make one a Christian, but having become a Christian, one is obligated to walk the walk. To not do so is sin. All but one or two sins are forgivable, but even forgivable sins will send a person to Hell if not repented.
As I understand it, because I am a Christian I want to do good works. I want to find ways to make people’s lives better, whether it be alleviating their burden or doing them small favours that adds to their life or teach them how to be more mindful of righteousness, but I cannot add to my salvation by doing so.
When you accept Christ, you now have absolute permission to do things differently and relief suffering. But it wont’ save you. It’s basically a by-product of your salvation.