Most likely not. Battery technology has come a long way, and the average cyclist can expect their battery to last for many years, or at least as long as the rest of their bike.
Modern e-bike batteries are designed to withstand hundreds of charge and discharge cycles while maintaining their capacity. Certain manufacturers guarantee a minimum number of charges and discharges before capacity begins to diminish: for example, Bosch states that their batteries are designed for an 8-9 year life-cycle with 1000 full charge/discharge cycles, and guarantees at least 500 full charge/discharge cycles over two years, before battery capacity begins to diminish. Of course, it helps matters greatly if you keep the battery in good health .
If we dig a little deeper, a full charge/discharge cycle does not include the ordinary ‘top-up’ charge that most people do in the normal course of using their bikes. It takes several of these ‘top-up’ charges to make up a full charge/discharge cycle.
Once battery capacity does begin to diminish, the battery will still continue to function but the amount of charge it can hold will begin to reduce over time, meaning that you will travel less distance on one single charge.The upshot of all this is that a battery can go through potentially thousands of charges while quietly soldiering on and doing its job.