Chek and see if the polygon mesh has edges that are categorized as border edges. Then if it has assume its open, it doesn't mean its open tough it just means its not logically closed. sSo you must now manually inspect the mesh.
This however is not enough, as having a fully closed polygon object still doent mean you can assume it will print out. Theres other things such as manifolds truncated ploys and lamina that can cause you to have even more serious problems than just being closed.
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No assurance with that method in terms of knowing whether all of the holes are found by doing that, so I would be curious to know if those resulting selections are in fact all of the holes.
No no ALL are closed if the object is selected, just not that all are closed in any sane way. So it might have been unlogically closed an you just blew in more problems than you solved.
As i said this doesn't not ensure success, it rather ensures slightly less likelihood of failure, not much.
