While r77 is supported by only su30mkk, mk2 and a smaller number of J11s, r27 is being used on a wide variety of chinese platforms. All the planes i mentioned plus all the remaining j11s, plus su27, j8ii, j7g, probably j10 too. I read some article mentioning there was some 3000 of various versions of r27 sold to china.
Bringing down an awacs is more or less impossible without casulties. It's hard to even predict what kind of fighter cover it'd have. But lets assume a lone carrier group, too far away to get additional air support (which is not quite realistic but to hell with it
) If it'd want to maintain 24/7 E2 coverage around the carrier, fighter cover for a E2 would be something like 4-6 hornets. (tomcats are already one foot (landing gear?) in retirement anyway)
They would stick with the awacs. Never too close so they don't endanger it, but never too far so they can't reach to defend it.
Plus, all the attacking forces would be seen on awacs radar. If they're asessed as too threatening, awacs would turn around and flee towards carrier, with its fighter cover either following it and keeping its rear covered, or staying to fight off/slow down/weaken the attackers. awacs could also shut down its radar if the enemy is close enough to launch a radar emission seeking missile. At that point they'd already know where and how many enemies are, and awacs is just running away to save its life, a new e2 is coming to replace it anyway, launched from the carrier after an interception force is launched.
So. Basically, there's little chance of destroying the awacs without having to go through its fighter cover. Basically you need a large enough force to do it with enough fuel left to afterburn your way in order to catch the awacs before the carrier interceptors come in range to protect it. Providing the e2 was so far in front of the carrier in the first place. It's quite doable.
Rinse and repeat a few times and carrier group will back off, if it's number of E2s is low enough. They're carrying 4 usually, but in a war situation like that it could go up to as much as 6. Still, they need at least 2 to maintain SOME sort of sustained air control (itd be much less of a radius around the CBG) and it's possible even that would be deemed too risky to stay.