China also has the non-inteference policy which would inhibit any military support unless their is an acute danger presented.
China's non-interference policy is moot if the government of Iraq or Syria openly requests direct military assistance.
All of these western pieces about the PLA joining the fight against IS is pure fantasy because there is nothing approaching a realistic attempt to present a convincing case for why China would want to spent all that money and risk the lives of its servicemen to fight an organisation, while vile, isn't really a threat to China.
Chinese nationals training and fighting with IS is a grave national security risk for China, just as western nationals fighting for IS are a major threat to their home countries.
However, the minimalistic military strategy America is perusing does not really present a convincing case to suggest such military action will lead to the swift, decisive and total defeat of IS. As such, Chinese security analysists should be asking the blindingly obvious question of what will China's involvement in such a conceptually flawed battle plan do other than make China a bigger target for IS retaliation?
In addition, even if China were to participate, there is simply no way in hell China will be treated anything like a real, equal partner. Chinese military officers will not be allowed into operational command centers never mind be able to influence military decisions. So in effect, what America wants is to for China to give it operational command of PLA forces and assets for them to direct as they wish. I'm sure American generals love that idea, but what's the upside for China?
Lastly, even if military success was possible, and even if US and Chinese military forces somehow manage to co-ordinate their efforts, how will the spoils of war be shared?
Again, China would demand a reasonable share of the spoils, with concrete and tangible benefits for China at the end of it, be it diplomatic, economic or military or a combination of those three. But once again, America would be absolutely loathed to give China any of that (just take your pick of all the bile filled rants about China being a winner of the Iraq war), and even if Obama agrees, China will have to be stupid to think Congress will honour any deals or agreements, especially a after Obama's term ends.
While it is entertaining to think of PLA jets, ships and special forces engaged in real live combat, that alone is nowhere near a good enough justification for war.
If Obama is serious about trying to get China to participate, his team needs to not only consider the points I raised above and many related and similar ones, but also come up with convincing and compelling answers to assuage China's concerns.
Trying to browbeat China with media sound bites is the exact opposite of what Obama should be doing.
At the end of the day, IS simply isn't remotely grave enough of a threat for America to be willing to pack away all its prejudice and amenity towards China, just as IS isn't enough of a threat to make China willing to swallow its pride and get bossed around by America for no benefit to itself.
America and Great Britian in 1939 were far closer than China and America are today, yet it took the threat from Nazi Germany, a surprise attack from Japan and the British giving their mostly closely guarded technological and military secrets to the Americans to forge the US-UK military alliance and get America into the war.
IS is a fart in the wind in comparison.