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Do you mean the actual battery or a battery grip?
1. Batteries. While its probably better and safer to use genuine canon batteries, there are many of us that use non genuine batteries without issue. It does also depend on the camera. Some latter models (5d2/7d/60d) use a smart battery. This has a chip in it that communicates with the cam and charger. There are a few 3rd party chipped ones around now.
2. Grips. A decent quality 3rd party one should be fine. You can get issues with bad fitting so the contacts move. If that happens you loose power to the camera . Again it depends on the camera. The lower end bodies the canon grip is made of plastic. While the 5D2 grip (maybe the 7D I'm not sure) are made of magnessium.
The genuine canon grips aren't the best made either. They have probably the worst designed thumb wheel to tripod screw gear system that you could come up with.