OK to use fallen branch in garden without treatment?
If you mean using it as part of a planter, then it will rot just as Doresoom has explained. Even if you treat it, the wood hasn't been properly dried which will cause other problems.

If you're just using it as a divider on the ground I wouldn't worry about it rotting. The rot will just supply the soil with nutrients. Since it's untreated, it's also safe for gardens that are grown for human consumption, as treated lumber harbors harmful chemicals.

I don't believe it will cause termites problems as long as it's not against any buildings. It's also a good idea to make sure the garden is not too close to your house, as the moisture from waterings can attract pests and encourage rot.