Welcome to this user forum for BT Retail phone and broadband customers.
Its up to you. There have been reported issues with the supplied batteries not being very good, and causing the phone to restart.
Its worth trying it off the base unit for a short while, and see if you can still make and receive calls. If not, then you would be best replacing the batteries.
It would not be very good if when you came to use it, the batteries were no good.
Remember you can still use your original phone, by plugging it into the phone socket on the back of the Smart Hub 2.
Hi @peter39 welcome to the community and thanks for posting. Yes, when the phone is not in use you can leave it on the base (charger). It will automatically stop charging when the battery is full.
Thanks
Neil