I am going to be backing up my current phone system and restoring it to a new VM instance in the same IP range. When I do the restore of a full backup, does it import the backed up IP address as well? Or does it allow me to keep the newly assigned IP address of the new phone system so as not to create an IP conflict?
Assuming you intend to upgrade to version 15, you can take a full backup of your v.13 server and try to restore it on 15.
Only FreePBX configuration is kept, not operating system. So you don’t have to worry about it changing the basic network configuration. I believe the only place you may have to fix IP addresses after restore would be in Asterisk SIP Settings.