The first series of Eurostars (373s) don't have 25kV connections, I don't believe. Each power car has a pantograph raised and the power car supplies power just for its own motors and the adjacent motor bogie under the first coach.
That does sound correct. Would make sense as well given the Tunnel's requirements (of the time) for degrees of redundancy with equipment, as well as the ability to split the train in the middle and drive both halves out separately.