From what I understand, it is possible for a third party app to trigger the same endpoints on Lemmy (either the search endpoint, or the resolve_object one), but it depends on how it is implemented. Boost might modify the search input before triggering the search, which would break the functionality.

I don't have a link handy to test with right now. You could also ask in !boostforlemmy@lemmy.world and direct them to this discussion. :)