search mode "Any word or synonyms"

My guess is it will just do the "Any Word" and ignore synonyms. Kentico usually codes things pretty logically, with future support in mind, so it probably does a check to see if Synonyms are allowed on the current language.

Nothing will happen. The configuration below is smart enough to recogonize it. Moreover your clause is an and query. SO it will search for "Anyword" and get some results however "Or Synonyms" will result empty set and the join over two sets will be set having results of "Anyword" only.

So in short, since there is no synonyms that you have provided so no synonyms will be searched for the query.

Thanks, Chetan