Do batteries on new devices start discharging even when plugged in to the adapter?
The device does not run on the charger. It will always run on the battery, unless the battery is not present. 

The discharge you see can be from just applications on the device running in the background. The charger stops charging the battery when it reaches full status. Note that this may not be 100%, even on a brand new battery. My battery doesn't charge past 96% any longer. Once it reaches that, it reports full and the device stops charging the device.

The device stops charging once the battery reports full so it doesn't over charge and damage the battery. This is why you probably see that the battery is at 98% after leaving it on the charger for a while. It does charge full (any probably to 100%, or close to it) but then the device stops charging once it is full. It wont just start charging the battery again when it drops below full, because this can also damage the battery if it was constantly charging/not charging the battery.