There is no limit. You can duplicate a bunch of bones to see what happens. After an unreasonable number of bones, maybe 2500 (the Metrics view shows how many bones you have), some actions might get slower, like filtering the tree or switching to animate mode. However, the action will complete and the rest of Spine likely continues to work just fine. The same goes for other areas. Spine scales pretty well where it matters though, eg all actions can be taken on this animation with 31,000 keys, without slowdown:

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One user had 50,000 attachments in his skeleton. Everything still worked, but like the above, some actions were a bit slow. We optimize things to where the app works well for a reasonable number of items for big projects, plus some head room. After that, it doesn't make sense for us to continue optimizing, so likely the app starts to slow down a bit, however it probably scales better than most software for various reasons. If you have a slowdown in a reasonable real world situation, then that is something we will improve.

You can run the packer separately from exporting skeleton data:
Texture Packing - Spine User Guide: Packing