Rechargeable battery in Ring doorbell 2nd gen - advisable to keep it connected?

I recently received a replacement Ring doorbell 2nd generation, with a rechargeable battery. Now the battery is freshly recharged and I was able to add it to my Ring account and have it work as it should. The Ring app is pretty lousy at alerting the user of a battery that needs recharging. It would just disconnect the doorbell and then you have to figure out whether it’s because of the battery or other issue. Would it be a good idea to keep the battery plugged in?