The ErrorString variable looks suspiciously like an error code variable. Recommended practice is to use exceptions to pass error information directly, where necessary, rather than storing things off into error codes.
You are effectively doing the same thing with your ErrorString as you would be if you just let the exception be caught by the caller: removing the responsibility of responding to an error from the method itself. This is a good goal to have. But the use of an error string doesn't gain you anything over the use of an exception. In fact, you lose information this way. There are any number of types of errors that could occur, and many have special exceptions associated with them, with their own special properties to hold contextual info about the failure. By just storing off the message in a String, you're losing this information.
So unless your goal is specifically to hide the type of error that is occurring from the caller, you can only gain by letting the exception through.
Another thing to consider is whether this is truly an error scenario. If it is, it's very unlikely that your calling method is going to care at all what the return value is. In which case, you have nothing to worry about by just letting the exception go and not returning anything. If it's NOT really an error scenario, and the caller is just going to continue on and do something else, well, that's for the caller to decide, right? There's still not much benefit to obtain by returning an error string and a dummy DataTable or a null, over throwing the exception with all its contextual failure info.