I'd have to say no to both questions. I remember my old Nokia 3310 wouldn't operate without a battery and you needed a special battery mount if you wanted to mess about with the ROM.
I think these devices are built with the assumption that there's always a battery, since the fabrication of test devices usually happens in some foreign production facility, and then shipped to wherever the devices are actually being tested. They are already complete products by this point so even any diagnostic hardware connections are placed away from the battery.
I think part of this is to do with the fact that USB is a standard unto itself. The phone takes the power input in whatever form it comes in, then uses internal circuitry to charge the battery at whatever current and voltage it requires to ensure proper charging, without wearing out the battery unnecessarily, or charging in in a way that increases the risk of it heating up and exploding.