In the pilot of Green Lantern: The Animated Series, Hal tried to recharge his battery off the Power Battery that powers the Green Lantern Interceptor. It seemed to work, but had some odd side effects. His ring was able to unleash a strangely powerful blast, and it appeared as though his ring was channeling energy from the battery. Normal Power Batteries just recharge rings, as far as I know. Have larger batteries ever been shown in the comics to grant rings abnormally powerful capabilities?
No, not so far as I have seen in reading the series.
Especially during Blackest Night and the War of Light, where the GL Corps were desperate for extra power, they never tried recharging from a bigger battery (though I think they may have charged from the Central Battery at some point, with no difference from charging from their normal batteries).
Interestingly, the Blue Lantern Corps are able to recharge a GL's ring very quickly, and they can charge the ring to well over 100% capacity. I clearly recall a single (or possibly 2) Blue Lanterns charging dozens of green rings to ~200% power (from below 20% levels).
Even in these cases, the rings simply have more available power (and can thus potentially hit harder), but gain no new abilities, just added stamina during combat.