Most 3DS games are designed to work on the old models (even newer games) and I highly doubt that they bring the much faster processor in the new series near 100% usage most of the time.
It might be possible that emulators max out the CPU usage constantly and that could be noticeable on running time (try out – compare emulator running time with normal 3DS game and share the results). However, I've read somewhere that e.g. Xenoblade makes the New 3DS get warm which means official games for the "New" series do use more of the CPU power.
The battery itself should be fine. Although common lithium cobalt batteries can be damaged by high currents this is not an issue if using consumer electronic devices. High currents means significantly (double-triple) more than 1C (c=capacity). That would be draining the battery in 20-30 minutes. No gonna happen on 3DS – even on highest brightness setting with maxed out CPU, WiFi on and volume on maximum.
Good luck and have fun!
Edit:
As for damage of the console itself: I don't think so (and don't hope so). A device should be able to handle 100% usage for quite a while. Heat can lower the lifetime of components and since the 3DS family has no active cooling I guess it could be a problem running them at 100% CPU/GPU usage in a really warm environment non-stop for weeks.