Absolutely, I just wanted to point out that e.g. China <=> Australia is most likely not considered it's own conflict, but rather a subconflict of China <=> US, as Australia is part of the US bloc, just like every other Western nation and close allies in Asia.
China <=> Russia would be considered a different conflict, as few people believe that Russia would be acting as a proxy for the US.
China <=> Russia would be considered a different conflict, as few people believe that Russia would be acting as a proxy for the US.