Can points not being passed to the loss function influence it?
1.Technically they are the same.They will compute the same loss. Although there will be a subtle difference in performance. In the first case gradient will only be calculated for the subset but in the second case gradient will be calculated for the whole training set but only the gradient of subset will be used to compute cost and update.
2.No, the points won't be invisible to the training procedure. the gradient will be calculated for all of the points but they won't be used.