flash for sports photography?

I will be shooting for an outdoor sport event at night, and I'm contemplating whether or not I should take my HVL-F20S flash for it. I've had experience in shooting sports for indoor venues and outdoor during the day, but there was enough light for me to maintain high shutter speeds.

Another issue I have is that the flash only allows up to 1/160s shutter speed. So I was wondering how the images will turn out given that limitation?

I'm using a NEX-5R, which has pretty good low light capabilities, giving me acceptable images even at 3200 ISO. But given that the event is low light and requires high shutter speeds, I'm not sure if it can handle the task on its own.

--
http://www.flickr.com/photos/kevinwlyu/