When entering air combat fighters usually jettison external fuel tanks and sometimes even dump internal fuel to lighten themselves. Then they build up speed&height (i.e energy) to achieve advantage over opponent. During air combat, they manoeuvre and lose that energy . In both cases better engine is an asset, because what engine really does is conversion of chemical energy from fuel to kinetic and potential energy (aforementioned speed and height ).
There is no doubt JH-7A could do hit&run attacks while avoiding close combat. But in that role even older 3rd generation fighters like Mig-23, Kfir or J-8 are better simply because they are faster (with upgraded avionics of course ).
Jettisoning external fuel tanks and dumping internal fuel to lighten themselves doesn't change my point. Your aircraft will still be limited by range, because when it has an air combat engagement, it is always going to have a minimum fuel level depending on the distance to the closest air base. You can win an engagement with your opponent by dumping 75% of your fuel, but it will be Pyrrhic if you'll end up crashing before being able to return to base.
Your aircraft will still be designed around the fuel level, because the T/W ratio and wing loading is not actually going to be constant for your aircraft, but instead will be variable depending on the distance between the airbase and the mission environment. If your aircraft is going to do short-range, you can choose relatively small wing areas to reduce weight, because you will not require large wing areas to provide low wing loading with a high fuel weight. Conversely, if you're going to do long-range, you'll need large wing areas to provide low wing loading with large amounts of fuel, and you'll also need high-powered engines to provide good T/W with high fuel loads and heavy payloads.
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As far as interceptor missions regarding the JH-7A, the JH-7A cannot do real stand-off missions with its present avionics. It needs avionics upgrades independent of whether it's going to do multirole or whether it's going to be a dedicated anti-ship missile carrier. Its radar system can only reach 100 km even outside of jamming conditions, and the US has long-range anti-aircraft missiles that have a declared range of 240km and can probably reach 300km. If the JH-7A is going to carry long-range stand-off missiles that can launch vs US Aegis Destroyers from long range, it will need avionics upgrades. And if it is going to receive avionics upgrades to enable it to feature stand-off capability versus enemy ships in realistic ECM conditions, it might as well have enhanced air-to-air capabilities built-in, as it features a 1000+mm radar aperture.