Sorry, but this is not possible. The closest thing I can tell you about is our rootKey
parameter of the category API. This query parameter would allow you to only return children of the category with the given key. The key is the second line in the contact form.
So if you send a request like this, you should get only a subtree of the categories:
/admin/api/categories?locale=en&flat=true&rootKey=category1
However, the bad news is that this query parameter is not used by the category_list
field type. However, a PR would be highly appreciated, and probably get merged :-)