justinflux: VODEMS & TSTICKS lose connection frequently and require physical unplugging/replugging when they lockup or overheat...
I believe it is due to the USB port (issues!!)
Charger should be fine as screen brightness will be low, and data use light
My only experience has been with Nokia's using Joiku Spot and I've been quite happy with them however as I mentioned before I haven't tried them 24/7.
The screen shouldn't need to be lit once it's up and running so the only draw will be the radio in the phone.
I suspect that some devices might "go to sleep" if there's no data transfer for an extended period of time probably based on the assumption that that connection isn't needed any more and it might as well save power. You might need to consider putting in a routine that ensures regular data transfer takes place to keep the connection alive.