The GH2 can do sports

I shot sports for many years with manual focus cameras without motor drives or winders. And got very good results. Sport Illustrated did the same, and got great results. But I doubt you'd find any SI photographers who'd choose to give up their 1D MkIV or 4D for a Nikon F2.

The better DSLRs are simply more capable for this purpose, and will (if used by someone who knows what they're doing) return a noticeably higher percentage of keepers. But yes, if the camera you have is an m43, you can certainly use it to shoot sports. It may require a bit of a different technique, and/or limit the types of pictures you shoot, but it will definitely shoot sports.

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OM-D for sale; see classifieds forum.