When plugged in, does the iPhone use the battery or the external source during heavy use? I love to play games and do other tasks that quickly drain the iPhone's battery. Sometimes I'll use the phone while plugged into a power supply. Does the iPhone still use the battery when performing these high-performance tasks while connected to the power source?
When you're plugged in to a power source, the iPhone will not use the battery unless for some reason you are using more power than the charging source can provide.

Normally, unless some process is hitting the CPU and GPU and all radios (such as a GPS mapping app), even a computer USB port at 500 mA will both power your games/apps and charge your battery at the same time. 

Even if your game takes more current than the charge is providing, using all the wall power will reduce the amount of battery being consumed which will certainly save your battery.

Of course, you should expect hundreds of full charge/discharges and as long as you are one a month draining the battery, you don't need to keep the electrons moving otherwise for good battery lifespan and health.