Will volunteer work or other co-curricular activities help my application?

These activities may help if they somehow demonstrate your research potential. For instance, if you have initiated and executed complex projects, that demonstrates you might make a strong researcher. 

The more closely related the co-curricular activities are to your area of interest for your PhD, the better. For example,  the ability to engage with communities  can be an important asset in conducting research in some areas such as Human-Computer Interaction and Computing Education