I'm wondering if it's possible to define multiple bevel objects along a curve and have Blender interpolate between the bevels like keyframes.
Nope, this isn't supported, nor do I think it's coming in any near future.
It probably wouldn't sit very well with Blender, since it's a mesh based. This would be more suited for NURBS based modeling tools or CAD software.
Closest thing I've ever seen is BSurfaces Addon but it's not a very good solution.