Does the crawler handle AJAX links (hashbang)?

Yes, for this it is enough to mark the corresponding option "index AJAX links".
Each indexed AJAX link should have an HTML version, which is available at the address, wgere the combination of "#!" is replaced by the "?_escaped_fragment_=" parameter.
In AJAX links crawler replaces the #! combintion to the ?_escaped_fragment_= parameter and accesses the page by the modified URL.
Links containing hashbang (#!) are used in original form when creating a Sitemap.