Does replacing an iPhone/iPad battery reset the battery stats?
The battery contains the "battery info", not the logic board. So if you put a new battery, what the logic board reads is based on the current battery only. 

Capacity and Charge are two different things. You're battery can be at 80% of it's design capacity but will still charge to 100% (of said capacity). It's just that a fully charged battery that is at 80% of Design Capacity will not last as long as a new battery that is at 100% Design Capacity. 

As far as your battery, it is at the lower limit. 80% of Design Capacity is okay but as you use the battery and as it ages, it will continue to degrade. The difference between an iPad and an iPhone is that we typically don't use the iPad all day so even if the charge is low a few days later, we just charge it when were not using it. On an iPhone, it is constantly in use (various radios) so we quickly notice reduce battery lifespan. 

Test your battery over time and when it gets below 70%, you may consider having it replaced but it will really depend on how you use your iPad on a daily basis more than anything else.