Of course. However, most PAP usually save hostages, round up drugs and traffickers, put down riots, guard important buildings or VIPs and blablabla...Others are engineers, for example, build railways, repair lines, search for gold, and Chinese firemen are also PAP. So PAP use shotgun more often. You can see them during Shanghai EXPO, armed with shotgun and SMG.
Actually, PLA are equipped with shotguns,type 97-1 , but they seldom use it.
I agreed with you here... What I am saying is that PAP don't act as SWAT. There are more to the Special Weapon and Tactic teams than just puting down rios, guard important buildings/ VIPs, round up drugs and traffickers, etc. In the US, polices (not necessary their SWAT teams), Secret Service and even FBI do the abovementioned task. SWAT teams are more like commandoes and special operation force equivalent to the Army's Green Beret and Navy's SEAL team - not really same in their training, etc, but their status is the same - all of them are Special Forces.
And yes, PAP uses shotguns more often because they are needed mainly for close quarter combat and Shotguns are excellent weapons for this purpose.
As to PLA, they might be equipped with shotguns, however why did they not using it as often might boils down to the fact that their missions are different as compared to the PAP.
My personal experience with shotgun is that I hated it... I hate the self pump feel of the weapon and I don't like the recoil. I would prefer a SMG anytime over the shotgun. But sometime shotgun is needed because of its stopping power. And it is very good weapon to use in fortified area... I can easily blast open a knob on the door or a lock using shotgun (I think) rather than using a pistol or a SMG.
And as to PAP doing guard duty in the expo armed with SMG and shotgun instead of assault rifle is the fact that assault rifle rounds had better penetration power and develope higher energy. So it is not good to use in crowded area whereby the rounds might simply penetrate one fellow, come out from him/her and hit others around him/her.
In this situation, you would want a weapon with more stopping power rather than high penetration power.