For example, I'm using a tree generator addon that creates trees in curve form. I have a strong wind forcefield in the scene as well for the grass. Is it possible to apply the curve to the physics?
No, I don't think it is currently possible, you'll probably have to convert your curve to a mesh.
If you are using the builtin Blender tree generator Sapling Addon it even has an option to create an animated armature with wind animation, but even then, has far as I know you will have to convert it to mesh to work anyway .
You may keep a copy of the original curve object in a separate scene or another layer in case you need to go back and change something.
EDIT It is apparently possible, although it does not work very reliably. Soft body physics can be applied to a bezier curve object, if it is well subdivided.
It seems most settings don't have any effect, except for the Self Collision options, as stated Quick Noodle Physics in Blender Tutorial Youtube Video
The trick is using a highly subdivided curve (there must be lots of vertex), and tweaking the parameters under Soft Body Self Collision like *Ball Size and Stiffness and turning off Soft Body Goal.
Some other object set to Collision Physics type must be present at the scene for interaction.