If using a Mojo why do you need to use it with a power supply? Just charge it overnight and use it direct from the battery during the day. You can use it whilst it's charging but it can get hot to the touch and long term it may screw the battery up but you can use it.
I'm not the Mojo's biggest fan, it does have a very relaxed sound though with plenty of detail but it adds a bit too much bloat in the bass and the treble is rolled off. However, depending on the headphones used it can sound very nice, I prefer it with the Senn IE300 but with the Senn HD600 and the Denon AH-D5200 that warmer sound is too much and it becomes bogged down. The Mojo 2 would be better as the sound is more neutral due to being able to use the EQ to adjust it.
I prefer something like the Topping DX3 Pro which is very nice all in one dac/headphone amp ad this does improve when you and an LPS to it, and it doesn't have those stupid balls and it comes with a remote which is pretty pointless as you'll be sat right next to it but it's the thought that counts. I also prefer the Sabaj A20d/h combo which is more detailed and neutral and much more flexible.