Does it work with custom post types and taxonomies?

Yes. Schema Pro lists every public post type and taxonomy on your site in a schema's Where it applies rules, so a custom one needs no setting of its own.

The rules a custom post type or taxonomy gives you:

• All {post type}, such as All Recipes: every post of that type.
• Archives: {taxonomy}: that taxonomy's archive pages.
• A specific post or page and A specific category, tag or term: one item, picked by typing its name.
• Every single post and page already includes custom post types.

An example: a site with a Recipes post type adds a Recipe schema and sets it to Show on → All Recipes. The name, image, description and author then fill in from each recipe, and a cook time kept in a custom field is read by setting that field's source to From a custom field.

A post type or taxonomy that is not public is not offered.