Does this include searching using the text search, rather than barcode? Does the search work if the user is offline?

Does this include searching using the text search, rather than barcode?

It refers exclusively to the local text search. Scanning a barcode or doing an online search (by hitting Enter) won't find these imported items.

Does the search work if the user is offline?

Yes.

So if I type "a" all the hidden foods containing the letter "a" will appear in the list?

Yes. If this is a problem, I could change it so these items only appear if you also apply a category filter. But then we would need to ensure during the import that the user selected at least one category to be applied to the items (because otherwise they could never be found).

I'm thinking it might be a little confusing because, when you don't press enter, the search box acts as a filter for the list of items you can see and when you press enter it searches for items you can't see. So revealing hidden items when filtering might be unexpected. But I think we should try it for now and see how it works in the real world.

I'm thinking it might be a little confusing because, when you don't press enter, the search box acts as a filter

I agree. I have now changed it so the hidden items only show up when the category search filter is applied. This makes for a much better user experience.