Upon hiding a field and reindexing JIRA it's no longer included in the search indexes and cannot be used to find issue. Records where the fields are hidden aren't even returned when searching for empty values. For example, if you hide components in a project that doesn't make use of them (let's call it NoCom) and search for issues across all projects whose components are empty, issues in the NoCom project won't be returned.

The behavior has changed from JIRA 3.x to 4.x. It would be useful to optionally have hidden fields be treated as empty when searching across projects.