I don't know about that, we have never seen J10s carry AAMs on its intake hardpoints, but theoretically there isn't anything stopping them from putting missiles there, especially not BVR PL12s which are dropped before engine start, so its not like the exhaust from the missile is going to present engine inestation problems for the J10 as you might experience with a rail launched IRAAM.
The flanker carries two BVRAAMs under its intakes in a similar fashion with the tip of the missiles protruding slightly in from of the intake after all, so it certainly looks viable. And the hardpoints can certainly handle the weight.
I am guessing that the J10 was originally designed to be able to hang missiles under its intake, and I do remember other scale models showing that. But we all know that the J10 suffered some intake strength issues after switching engines midway during development which led them to have to jerry rig those side support brackets. So purhaps that is why we very seldomly see those hardpoints used at all, because to hang loads under those hardpoints regularly with subject the already weaker then desired intake joint to additional stress and strain which might cause maintenance issues or even shorten the useful lives of the planes significantly.
However, an interesting question would be whether such a capacity exists but has never been show off in public before for the above reasons, or whether the potential for the option was originally designed in, but ultimately never exercised because of the above list reasons.