NIC won't improve your play quality in the slightest. In AH, latency is more important than speed. Even if it wasn't, network speed is only as fast as it's slowest component.
The slowest network cards mostly in use are 10MBPS.
The fastest broadband connections are typically in the 5-10MbPS range.
If you upgrade to a 1000MBPS card yes you'll have a faster speed between your computer and your internet connection, BUT you'll still be limited to your internet speed which won't even come CLOSE to the 1000. Waste of money if you ask me, unless you have a local network transferring a lot of information.