independent variables in Random forest model

Is it reasonable to run a random forest model with an independent variables that has almost little or no variations. How they impact the model and whats their role in predicting the dependent?from technical point of view I believe they will not be used in building the tress and will have no role in predicting the DV

• If a variable has little variation, it can still have predictive importance. This should be obvious: if all values of a feature larger than some constant $c$ corresponds to one class, and all other values to the opposite class, it's a really good predictor. (Likewise, if it's completely independent of the class label, then it's worthless.) This is true no matter what the variance of the feature.