Animate a sine wave in Unity using bone rotation?

I have imported an .fbx of a long cylinder with 5 bones (which are now objects) positioned in a straight line.

Is it possible to simulate a sine wave by updating the rotation values of the bones in that mesh through script?

Yes. Bones are just Transforms, in Unity, so you can alter their rotations (although I think positions would be what you need for a sine wave, unless I'm misunderstanding the effect) as you like. Transform.Find will probably help you most, in acheiveing this, because unless you create the mesh procedurally in Unity, you won't know what is what, in the SkinnedMeshRenderer.bones array.