Only if you're flying a Flanker off a ramp, look at the Su-33 load-outs that went to Syria, they were light, because that's all the SU-33 wanted to carry off the ramp, J-15 specs are very similar, same basic powerplants and airframe, which may? be a little lighter due to the use of composites?? that's the active narrative here on SDF.
Check the load-outs on the Mig-29Ks that went to Syria as well, I realize that the Mig-29K was flying strike missions, but it would carry a very similar load-out for A2A.
If you are expecting trouble, and you're operating off a CATOBAR or a land base, you load em up,,,, Flankers and F-15s will haul a lot of air to air missiles, check those additional hardpoints.
In peacetime, when you're basically just orbiting the carrier flying "top cover" or CAP, you might only carry 2 to 4 AAM, wartime, no way, you're going to fill-er-up, NOBODY goes to a GUNFIGHT with only two to four rounds in the magazine, NOBODY!
If you are operating a 5 gen, you would load it up with everything you could carry internally on the 1st Day, after those Air Defenses are cleared, then you would install hardpoints and "Load-er-up"??
I don't think the J-15 is very limited in AA missiles though. We know they can carry at least 2 YJ-83s and 2 PL-8's at the same time, and since each YJ-83 weighs as much as about 4 PL-12s, that would be equivalent TOW of 8 PL-12s and 2 PL-8s, a full CAP load out for the J-15.