It will not damage your battery.
It will shorten its life though, but there is nothing practical you can do about it.
Lithium Ion batteries age in two ways, one is through what is termed “Calendar Life” and the other is Cycle life. Here is what you need to understand about both:
Calendar life – the time spent at a given state of charge (SOC) and a given temperature causes a loss of capacity and increase in internal resistance that is proportional to the square root of the time. Higher SOC imparts greater degradation. Higher temperature imparts greater degradation. Keeping your computer plugged in all the time with the battery ensures that the battery stays hot and charged as much as is possible. If nothing else, turn down the performance of the laptop when you don’t need it to overperform so that it runs cooler.
Cycle life – while you might think that it makes sense to fully discharge the batteries, rather than put lots of little cycles into it, the opposite is true. Lots of little cycles do virtually nothing to the cells. 100% discharges are the bane of their existance.
So, the reality is, you could optimize battery life by keeping the battery about 50% charged, letting it discharge a bit and then recharging it, and if chargers allowed for it, floating them at a SOC that was not 100%. However, it is much much easier to just get on with life and use your laptop and not worry too much about this. Assume your battery costs you $1 a day. Put that much away for its replacement. When it is fine on the day you buy your next computer, you have now paid for that new computer, or a good size chunk of it.