I don't know for sure, but I would think that he would be able to run while plugged into an outlet as that would be much easier for the developers than constantly recharging him. I was told that this Pleo was used to test out animations on a physical model, so it seems like more so a "testing" prototype than one that was meant to run on its own. I don't have any actual proof though that he was intended to be able to run while plugged in.
The Pleo arrived to me in a different position than in the listing photos, so it's possible that the previous owner who worked with him had some way of operating him, but it's possible he could have just carefully manipulated all of the joints to make the Pleo better fit in the shipping box. The seller described both prototypes that he owned as "currently non-operational." I did not receive any accessories with the Pleo, so the only power cord I've been using with him is the one intended for a Ugobe charger. The charging port on his chest says "12VDC 800mA" next to it which is the same specs as the regular Ugobe charger. He makes a soft pinging sound when plugged into the charger, but that's all I've ever gotten from him.
There is another port next to that one that I do not know the use of and assumed was used for programming him directly from a computer, but I guess it's it's possible that this could also act as a power source and the other port may only be for charging the internal battery. Although, it is possible this prototype simply was never able to run while connected to an outlet since the older prototype listed by the same seller had two ports that looked like they were for charging, while this Pleo only has one.