I don't believe it should affect the performance of your machine, but it is possible that if the battery is dying, it could be putting some surges into your machine, risking damage to the hardware. Most laptops have decent protection against this, but I'd recommend you pull the battery and run on AC.
The only way that I could see this affecting the performance of your machine is if you have software that monitors battery charging, and the battery is quickly charging/uncharging and the monitoring software is changing modes to keep up, eating all the CPU.
If anything, this also would let you know how the battery effects the performance of the machine. As SNGX1275 and I said, I don't think you'll see any performance issues directly caused by this, but it's not impossible.