We don't have anything built-in. But that should be doable.
This is uncharted territory as far as Spine-Unity users go so you'll have to make it up as you go, and find out the limitations yourself. There's a possibility that your meshes are very complex too, and the memory you're asking for is huge.
Unity already has a Mesh
object type so you can probably just store that.
What you would do is pose the skeleton, have it render the mesh, then get a copy of the Mesh from the MeshFilter component and store it yourself.
It would probably look like:
skeleton.SetToSetupPose(); // Reset the skeleton.
animation.PoseSkeleton(skeleton, time); // Pose at a specific time using an animation.
skeletonAnimation.LateUpdate(); // renders the skeleton.
meshArray[i] = Instantiate(meshFilter.sharedMesh); // get a copy of the mesh and store it.