Have a look here Help enabling HTTPS on admin interface - #2 by sitloongs
A public certificate authority can not assign certificates for a private IP address. The way some vendors do this is to set up a default DNS entry that can be used to access the device locally and then produce a self signed cert for that fake domain (ie https://mydevice.peplink.local) which is far more insecure in my opinion.
Yes it should be added.