No extra managers run in the background, even with Spine GameObjects in your scene. So no. Including the library by itself doesn't consume cycles.
Only updating meshes and applying animations requires processing per update. That only happens in SkeletonRenderer/SkeletonAnimation/SkeletonAnimator.
The amount of CPU processing it requires depends on things like the number of vertices, bones, dopesheet timelines you use.
There are many extra things you can do/remove to improve performance but that's micro optimizations you don't need to do until you check the profiler and know that's the bottleneck or, at the beginning, the actual thing slowing down your game if it slows at all.
"Colossal sized bosses" with pixel art are more likely to eat up fillrate allowances than be a CPU hog. The more pixels each quad/image/part occupies on screen, the more GPU power it requires to render. This is true even for a static mesh, in any engine.
What do you mean by "swap sprites on a palette"?