Silly question: I believe I’m correct in saying that the front-end ee search does not search the gallery?

How about the back-end search (in the ‘edit’ pane)?

If the answer is no, can this be moved to a feature request? Thanks.

Correct- the gallery isn’t searchable yet.  I’ll go ahead and shift this one over to ‘Feature Requests’ for you.  (Note- if you poke around the backend code a bit, you’ll see where there are gallery search related elements, so it’s looking like the dev crew has been working on it.)