In feature selection for predictive models, it is usually applied a permutation test. In this test, all the values of one variable are randomly permuted and the prediction accuracy is extracted for each permutation. For example, if we have 3 variables (features), the ACC with all variables is 0.9. And, in the permutation test, we get ACC of 0.2, 0.1 and 0.9, respectively, when the first, second and third variables are permuted. Thus, the third variable can be dropped because it does not help for the prediction.
However, if we delete the variable or change all the values to zero, instead of randomly permuting the values, do we get the same result as for the permutation test?