Not a teacher, nor a native.
I would also replace a full stop with a comma there.
Should that happen = if that should happen, that is nearly the same as if that happens, but with should, the speaker feels that the possibility is smaller.
I can see that idiomatic means both expressions that contains idiom and expressions that are natural to native speaker.
Not knowing which of these you meant, I can give you an example I came across reading a brochure:
Should you become a victim of a crime, call some number.
So I guess it is natural to native speakers.
Interested in Language