Can a parallel universe Earth without reliance on modern technology make any progress?
Maybe in the parallel universe people ARE the technology?
No, or I should say, only up to a very unsatisfactory point. The Greeks did perfect the trireme, the Phoenicians the art of navigating by the stars, the Vikings the ocean-going Longship, and the Renaissance Europeans the long-range galleons, but what are those primitive ships compared to an aircraft carrier or a nuclear-powered submarine? The North American Indians barely progressed past the Stone Age, when left to their own devices. No, technology is the essential component of modern progress in any meaningful sense of the term.
I'm not sure I understand the question. Can it make technological progress? Social progress?