I'd say "no, it's not good enough", but it's hard to rule it out absolutely without knowing more details about you're going to try using it. To take each of your three use cases:

• Wildlife: probably not enough reach. You're looking at 400mm or more for typical wildlife photography.
• Football: If you can get somewhere near the sidelines, 200mm probably gives you enough reach to cover the near half of the field. f/5.6 will be fine for daytime sports, but won't be useful under lights.
• Gymnastics: too slow. It depends a lot on your gym and how close you can get to the action, but if you're at f/5.6 then you're probably going to be around ISO 6400 to freeze the action - and that's marginal at best on a crop sensor.

Stepping back a bit, there are two significantly different categories of photography you're trying to cover here: wildlife and (daytime) outdoor sports, which require a long focal length but not necessarily that fast a lens, and indoor sports, which don't require such a long focal length, but do need a fast lens. Don't expect to be able to manage both of those with just one lens.