The basic idea behind baking objects is that it converts them to native Unity objects. This means after baking, your objects no longer rely on the Spine runtime to function (I believe the video references this).
Being fairly new to Unity and Spine myself, I'm certainly no expert, but I would probably say not to bake your objects unless you really have a reason to do so. There are some cool elements to the Spine runtime (check out the features on this page: viewtopic.php?f=3&t=3318 ... Thanks, Mitch!) that you lose out on when baking. (I'm sure some more experienced Spine/Unity users may disagree with me on this 🙂 )
As far as getting things to work the way I was suggesting, I just tested and confirmed that the animation controller does update correctly. Here are the steps that I used (note that I am using Windows and Unity 5, although I'm pretty sure this worked the same in 4.6):
1) Export your animation from Spine and import into Unity (I usually just do this by dragging the files from Windows Explorer into the project window in Unity).
2) Right click on the SkeletonData.asset file that was generated, and click Spine>Instantiate (Mecanim). The object is added to the scene. Note, also, that an animation controller is added to your project that contains your animations. This animator is also automatically associated with the object in the scene.
3) Make a new animation in Spine and re-export
4) THIS STEP IS IMPORTANT: Open your Unity project folder in Window explorer (right click on any of the Spine data in the project window and select "Show in Explorer"), and in another Explorer window open the location where you exported your Spine data. Copy the atlas, png, and json files FROM the Spine export folder TO the Unity asset folder where your old Spine data exists. This will probably ask if you want to overwrite the files, and say yes for all files. (As a side note, I tried dragging the data directly into Unity, but this simply created a new copy and did not update the data that was already there)
At this point, when you go back to Unity, the data will be refreshed, and the animator controller that was already there should be updated with the new data (including your new animation). Additionally, the state machine (the animations and transitions) should be preserved, and you can simply drag and drop your new animations.
Hopefully that made some amount of sense. Let me know if this process works for you. If not, I'd consider making a video tutorial if that would be useful to you.