To the phone it will do no harm although you should think about if you want to follow battery-health-suggestions about using battery only between 20-80% of charge…then overnight is no choice (btw: does anybody knows a trustworthy app which can handle this automatically?)
I just want to share additionally to here, that my original FP1-charger consumes 1.5Watts if the FP2 is plugged-in, power-off but already reached 100% charging - which is quite high (in comparison to nearly 0.0W if the charger only is plugged-in without a FP)
I will compare it later to the powered-on-FP2…