When creating a classification model, should predictors with little correlation to the response variable be included in the model?
In general, a Kruskal-Wallis test (or any other univariate test) cannot guarantee that there are no useful interactions with other features that a decision tree might still pick up. That means you won't know for sure until you try it.

You can test the performance with and without these "weak" features and compare results. Make sure you control for overfitting when including all features. Alternatively, after fitting the decision tree, you can look at the target response when varying the feature values ("partial dependence").