XNA does not support animations out of the box, to get animations in you need to write your own code, such as the skinned sample they provide. Changing that sample to instead load a number of FBX files and changing between them with morphing is quite possible, its used in some games and demos to do facial animations since it provides the artist with more finegrained controls.
There are drawbacks of course, the animation will take more memory since it needs to store the entire model 100 times (for your 100frame example above) instead of just the changes in terms of bone animations. But as long as you use it sparingly it shouldn't be too bad.
The first step is to export the scene into a suitable format (FBX), you need to do this once per frame (or once per keyframe, the further apart they are the higher the chance that the morphing will look bad). I don't know how to do this in 3DS Max but hopefully it has a batch mode for exporting or some scripting API you could use for this.
Secondly you need to write a processor that loads and combines all the FBX files, a quick search gave this post as a possible example, in this case it has a flaw about multiple different textures but its a starting point.
Thirdly you need to animate the result, I would recomend looking at this CPU Gem chapter which is about facial morphing.
As you can see, it isn't entirely straightforward to do, in the end it might be simpler to simply rig your animation, but morph targets can be a very nice technique for good looking facial animations (in particular) so the time spent researching this won't be wasted.
