Yes, sort of. The normal way to have a post process that only applies to one camera would be using a scene capture. Let me link some references here:
In our Content Examples, we have a Post Process level and a Reflection level that could help you figure out how to do this. The short version is that you create a material that includes a Render Target as the texture (so it constantly shows a particular view of the scene), apply post processing effects to it from the Scene Capture, and then you can display that material by placing it in front of the camera, for example on a static mesh.