Yes, the ODIN GPS-03 can be permanently connected to a power source and will still continue to work. You can, for example, connect the tracker to an external USB powerbank (for mobile applications) or to a permanent USB socket in a vehicle (for modern cars). When the power is connected to the tracker the internal battery will get charged, and when the power is disconnected the tracker will automatically switch to the internal battery.
It is also possible to permanently connect the ODIN GPS-03 to a 12V power source by using a generic "12V to 5V USB adapter", which you can buy in many online stores. This, for example, will allow you to permanently connect the tracker via USB to a car battery.