Should I use hashbang/shebang?

Question

I read here that the idea of the shebang (#!) was so Google

knows that an alternative conventional URL exists providing the same page "state"

So, if I don't have conventional URLs corresponding to these hash-states, am I right to say that I should be using just a hash and not a shebang?

Background: The hashes are created based on a search form, and the search results are loaded on the same page. The hashes are there so that people can go back to the URL with the hashes and repeat the same search.

More broadly, is there a reason I should have real URLs corresponding to my hashes?