They would have wound up in the hands of rich collectors, where they'd probably be a lot safer than they are in Baghdad right now, a few hundred km from an army which would happily destroy all pre-Islamic artefacts.
Especially this one, which is a story with other gods in it! Can't get much more unislamic than that...
So yeah, as long as ISIS or any of its successors never takes Baghdad it's safe. I'd rather it were in some rich dude's house though.
Baghdad is still relatively safe, but could be better. I could see them loaning it to the National Museum at some point, but only temporarily, and not for many years.
If they make it to a museum, then the information on the tablets becomes public and therefore very safe. Discovering and preserving the story is more important than the physical tablets.
Especially this one, which is a story with other gods in it! Can't get much more unislamic than that...
So yeah, as long as ISIS or any of its successors never takes Baghdad it's safe. I'd rather it were in some rich dude's house though.