I made a character and added toon shading but I can't see it. After some research it seems that toon shading is only visible if you render the image with a camera in the blender scene. I want to import the cel shaded model to Unity so I have to need for a camera or light source since I will have to use Unity's. Is it possible to export a "cel shaded" character?
Since a shader is calculated real-time, and not something that can be feasibly stored and exported, this is not possible. Unless unity has a feature to interpret blender's settings and simulate blender's toon shading, which I don't think it does.
I've never used unity, but this pretty much applies to importing and exporting to/from any program.
I cannot say for certain if it can or can't be done, but I would advise against it regardless. Unity comes with a few toon shaders that are fine for most cases and are guaranteed to work with the engine.
What you do instead is that you export the mesh object by itself and build the material you want for it inside Unity. You also assign the texture for it in Unity if your object has one.
If you feel you need more control over the toon shader, there are some solutions over at the Unity Marketplace you could try.
For a toon shader to keep it's appearance based on camera angle you will want to use a unity shader.
If you want to use blender's toon shader to define a static appearance then you can bake a texture in blender to an image and use an image texture in unity. While baking is most commonly known for creating normal or bump maps you can also bake out entire textures as well.
Bake options are available under the render properties panel and up until 2.70 are only available for the blender render engine. Cycles baking is currently in progress to be included in 2.71