I liked the movie. But for the TV show... it got better with age because they got more money for effects as the the series got some success. But in the beginning seasons, everytime I saw those cobra helmets on the bad guy soldiers, it reminded me of Dark Helmet from Spaceballs. It was so cheesy with that visor flipping up and down. It was nothing like the morphing effects in the movie with the jackal and bird head dresses.
One thing you need to know about science fiction... it's usually an epic wet dream fantasy of the creator. Meaning science fiction is a Freudian glimspe into the mind of the creator as how the world (in this case, universe) should be. So, you'll either see China in the SG-1 world play nothing more than a subordinate role if they're on the good side or play the antagonist enemy (that will always eventually be foiled and beaten) on the bad side. So as for the hypothetical question... China would never able to claim anything and certainly would fail at the attempt if they even tried.
Very few science fiction stories actually try to predict "the future" with educated deductions. I'll give this to SG-1 that they'll actually include China as somewhat of a power in their universe. But for the accolades given to something like Star Trek for its "positive" view of this world in the future... yeah, in your wet dreams it's positive. I like Star Trek as entertainment, but for those that try to make it out as something as a social statement, I've got a problem with it. The West obviously took over the world in Star Trek. They're only 15% of the world yet dominate the universe? Ironic, if they actually tried to portray the Star Trek world with some social realism, it would probably be not the success that it is because it would not have a Western-centric theme and cast. C'mon, no Western country can live under the rules of the "prime directive."