Yes.
The SignWriting symbols directly represent handshapes, movements, and facial expressions. Because these things are the same for every person in the world, SignWriting can be used to write the sign language of any country.
The International SignWriting Alphabet (ISWA) defines a single set of symbols which support all known sign languages in the world. However, a given sign language typically does not use all of the ISWA symbols.
For instance, the ISWA defines separate hand symbols for 261 distinct handshapes. But written American Sign Language (ASL) uses only 86 of these hand symbols, since the ASL language does not use all of the ISWA handshapes.
For more information on the SignWriting symbols see "Textbooks" in the Library section of this website.
Library > Textbooks