Therese Radic, Songs Of Australian Working Life, has the song, Freiheit, and these notes:

"Although only a handful of Australians volunteered and fought alongside the Spanish republican forces, the inspiration of the International Brigades gave a new significance to the songs of the socialist movements of many countries. Right up to the 1950s songs such as 'Freiheit', from the German International Brigade, 'The United Front Song' (Brecht/Eisler), 'The Peat Bog Soldiers', and the Spanish song 'The Four Generals' were popular as a confirmation that the Australian labour movement was not isolated."

So it appears there was an impact, but the extent of it was an appreciation of the songs written by others.

(I am not an Aussie, but I play one on the internet).