No they are not related.
Battery Cycle count is irrelevant to determining battery health except when it gets high and nears 1,000 cycles. If an Apple Lithium battery is nearing 1,000 cycles, then it will likely need to be replaced soon. A low cycle count is meaningless especially if the laptop is always connected to a charger since this will keep the cycle count low. The actual age of the battery is a bit more useful for gauging health, but again just in a general sense. Many Lithium batteries can go three years before needing replaced, while others may go to five or seven years, while some may fail in less than three years. Generally if the battery & laptop are well cared for, then many batteries will last 3 - 5 years.
The more important factor in determining battery health is whether the Full Charge Capacity (FCC, aka "maximum capacity") is at or below 80% of the original Design Capacity. Apple won't replace a battery unless the FCC is below 80% of Design Capacity (unless a hardware failure has been detected by macOS or the Apple Diagnostics). Many people still are happy with the performance of the battery even when the FCC is below 80% of Design Capacity, but it all depends on your needs. Basically just use the battery until the battery is no longer performing to your expectations. Then check the Battery condition by Option-clicking the battery icon on the menu bar to see if the battery condition is listed as "Service Recommended". If so, then it is time to have the battery replaced since you are having issues and macOS has determined either the FCC is less than 80% or macOS has detected a hardware issue with the battery.
If you have an Apple Silicon Mac, then macOS already shows you the FCC value. If you have an Intel Mac, then you can use a third party app like Coconut Battery to keep an eye on the battery "health" and FCC value.
Keep in mind that the battery condition reported by macOS, the Apple Diagnostic results, and third party app like Coconut Battery are not always good indicators of battery health since they don't always detect some battery hardware failures. There have been many times when all of these indicate a healthy battery, but when I perform some special monitoring of the battery I can detect signs of a failing battery.
