yes, the Mini-T does have an on/off switch on a side, so that would save the battery from draining. this version is only battery powered though (probably will remain this way) at least for this model, so no MIDI powered i’m afraid but at least it would save you from having an extra power supplier connected 
for those interested, i’ve been working on a new version of the Mini-T. it will have pretty much the same form factor of the non USB version. still finishing up the firmware (not sure whether it’ll also pass SysEx messages or not though…more to come… )