Matlab can handle highly correlated inputs. However, if you want to interpret the output in terms of the inputs, you can recursively remove redundant and ineffective inputs from a linear model using STEPWISE or STEPWISEFIT.
It depends on what you mean by performance. My intuition tells me that correlated input variables should not decrease network accuracy, but will increase network redundancy (and as a result may increase training time).
Since this question is not necessarily specific to MATLAB, I would suggest posting to other sites as well if you want to reach a broader audience (e.g.Cross Validated,StackOverflow).