In some cases I think it does help to protest and take to the streets and not only strike. For example striking dock workers and metal factory workers is one thing. Having them march on the capital is another still... There's definitely overlap between these groups of workers and soccer hooligan groups for example. A large protest of certain groups imply the promise of non-state controlled violence if agreements aren't reached.
Other case is when the protests is just really really big. A few hundred thousand does work to get the message spread more clearly how 'willing' they are to keep striking. While striking and just sitting at home during strike sends rather mixed signals.
It also enforces the "we're in this together" in the workers.