Will the readings of the potentiometer be affected if they're not grounded?(like erratic values, or higher fluctuations)
No.
Grounding pot bodies is important in audio circuits.
It is not that important, it is done :-
- Because it can be done
- It might reduce pick up of other signals that are inject into audio circuits
The bigger the pot value the more prone to pick up it is. You are using about 10K for your circuit which is low impedance for this sort of worry. In an audio circuit you might be using 1M or bigger which is more prone to pickup.
Bottom line. Don't worry about it.