You can absolutely do it. Lots of very successful athletes are and I have, too. In the first few weeks of the diet you may find you're not at your best, actually many experts recommend not starting an exercise program for a week or two after starting the diet. According to Volek and Phinney, full keto-adaptation (getting to where you can train more vigorously again) can take about three weeks, and you have to stay strict with the diet. You should read their book "The Art and Science of Low Carb Performance".

I'd start real slow (I follow Mark Rippetoe's training instructions in "Starting Strength", another great book), and expect a boost in strength and performance after about week three/four. Make sure you eat/drink enough salt, by the way, this diet has a diuretic effect and low salt can make you feel weak!

Endurance athletes are doing it too, by the way, Chris Froome of Tour de France fame, for instance! I saw that in the news today.