> (defun isearch-cycle-search-invisible ()
> "Cycle the value of `search-invisible'.
> Bound to \\<isearch-mode-map>\\[isearch-cycle-search-invisible] in `isearch'."
> (interactive)
> (setq search-invisible
> (case search-invisible
> ((nil) t)
> ((t) 'open)
> (else nil)))

I personally find the "search within hidden text without opening it" to
be a completely useless option, so I couldn't want to cycle between all
3 options, but only between nil and `open'.

> (define-key isearch-mode-map [?\M-i]
> 'isearch-cycle-search-invisible)

You'll have to place it in the M-s prefix map instead, which was setup
specifically to avoid eating up more key combinations which currently
make isearch exit.

> So, it would be good if the user could change the value of
> `search-invisible' as well directly from isearch.

I'm not sure I'd find it useful, but I can imagine some people might
like it and there's plenty of room under the M-s prefix for such
a thing.

It is in my opinion very useful in org-mode.