Wouldn't it get diced by the prop first?
No, not at all. Birds can go through, or around the prop. When I was doing aerial application (crop dusting), I hit hundreds of birds throughout the season. Making it past the prop to strike the windscreen wasn't unusual at all. Often the birds would hit the large blade that ran upthe middle of the windscreen, and get cut in two, or they'd ride the blade to the top of the cockpit where they'd enter the fresh air intake. There, they'd usually explode and get blown all over inside the cockpit.
A light on will help make you more conspicuous to the bigger hazard; other aircraft. It likely won't do much for alerting birds. You'll hear similiar tales about using weather radar for the same purpose, but it's myth.