Long range AAMs on the 022s are indeed unlikely, but mostly because they will be largely pointless.
As others have already pointed out, targeting and guidance is going to be the primary problems.
There are extremely few scenarios where it would be useful to be able to pop off SAMs a few hundred miles ahead of the nearest friendly dedicated air defense asset.
You might be able to sucker punch some income strike aircraft, hitting them before they think they are in danger. But that's a massive gamble, as placing 022s so far ahead of friendly support would leave them exceptionally vulnerable. And it's a one shot trick, if that. You do it once and the enemy will be wise to it and sweep ahead.
On balance, it's just not worth the hassle.
They might make a test ship or two just as a proof of concept test for co-operative engagement, which they then could use as described above to troll an enemy during combat and make them waste time and resources sweeping for SAM carrying 022s ahead of every strike package. But it won't be something they will devote anything like meaningful resources or numbers towards.
A more interesting and practically useful conversion might be to fit land attack cruise missiles on the 022 and base them on the new islands build in the SCS as survivable mobile long range strike assets against hostile land bases like airfields and Coastal defense missiles without having to use up valuable VLS cells on larger warships, which would be much better served carrying SAMs.
During a strike operation, you use up a lot of cruise missiles very quickly. Rather than sending one of your small number of top DDGs or CGs all the way back to a mainland port to rearm, which will take days and take its powerful radar and battle management systems with them, they could just sent a dozen 022s back to one of the new island bases and have them rearmed and back in the fight within hours.