O yes, but he's more likely to be the one carrying the baggage than the fellow at the front of the procession with the fancy duds and the silver tongue. The Lord's among us, all right, but not necessarily as the chair of the committee. He's more likely to be the one who locks up and takes out the garbage. There are lots of ways of governing the church. As much as I love the Presbyterian form of government, I doubt whether God cares much which one we use.
Some churches use bishops.
Bishops are efficient, I suppose, but their heads tend to swell to fit their miters. Every form of church government is flawed. Each is capable of fostering extraordinary faithfulness and equally extraordinary cowardice. All fall short of the glory of God, and yes, God works in and through, and even despite of, every one of them. That's because the Head of the Church is not the bishop, or the congregation, or the session.