This is unofficial:
1) Spine does things that Unity's built-in animation system can't, so it doesn't really work by saving as native UnityEngine.AnimationClip
s.
It has its own data structures and things. This means you can't use Mechanim as the the animation controller out of the box.
But Spine does do crossfading/"mixing" and multiple, simultaneous animations on one skeleton out of the box.
This said, my guess is that it wouldn't be too difficult to make Spine's system interface with Mechanim's animation controller. Nobody has posted about it here though.
2) You can export to spritesheets. This was a recently implemented feature.
But by using it this way, you'd mostly lose the strengths of Spine's skeletal animation at runtime: (1) save you GPU memory and (2) allow your animation's framerate to be as high as the actual game's framerate, and (3) programmatically control body directions and (4) mix multiple animations— features that most 3D games take advantage of.
But using spritesheets does mean that you wouldn't be using the Spine runtime and thus your first question wouldn't be applicable at all. You'd just use Unity's animation system to flip through the spritesheet-exported sprite and it would work fine with Mechanim.
But if you know that's what you need, then yeah. Spine editor can export to spritesheets.
I wonder if you weren't actually thinking of atlases.