Unlikely. Kindles are e readers that last a long time. I have a 10yr old paperwhite as good as new!
Mine is only like 2-3 years old and I charge it so rarely. I can read several entire books on a charge easily. It lasts months. I imagine even if the battery degraded significantly it would be quite usable.
I was also having a play with a demo model of the latest one in a store and the page turn speed is much much better, which is tempting me to upgrade though I'd prefer to run the current one into the ground first.
Its a Lithium battery so unless you let it drain to single digits every time, it'll last a LOONG time