Does Non Negativity Constrains increases the estimation error
Are you talking about train error or test error?
Non negativity constrains make your search space of possible solutions much smaller. This means that the train error would be always higher or equal when you add non-negativity constraint. 
But higher train error can mean that you are overfitting. If the assumption of non-negativity make sense for the solution of your problem, then it is likely that this assumption would decrease the test error as you are limiting your function space and decrease the chance of overfitting.