Unfortunately, the answer to your question is machine dependent. In short, you don't have to worry about your events getting "lost" as they are queued up internally so each event will be serviced in order as soon as the processor can handle the event. However, the speed at which the processor can service each event is a function of both the processor speed and whatever else is taking up processor cycles on your machine (e.g. other applications). If you exceed what your processor can handle, you may observe what appears to be your system hanging, as it cannot respond to anything else because it is too busy servicing interrupts. This prevents the CPU from doing anything else, including updating your front panel GUI.
1000 Hz sounds like a perfectly reasonable rate at which to run your counter output task, but understand that your performance or application execution timing may change if your deployment system is not the same as your development system.