Certainly not. The alphabet has been copied "as is" from Swedish, and it has been so since Mikael Agricola began writing Finnish. Fortunately the Swedish alphabet contains enough sounds like Ä and Ö that Finnish speakers didn't have to design any new letters. Then again, unused letters like Q and Å remain. The last changes to Finnish orthography with respect to the alphabet were the changes from 'C' to 'K', 'X' to 'KS', 'TZ' to 'TS' and 'W' to 'V', in the 18th and 19th century. 'C', 'X', 'Z' and 'W' remained in the alphabet but were no longer used.   

š & ž