Sam,
Yes, duplicate nodes at the same location are not, themselves, connected. So, any things that are connected to the different nodes can't talk to each other, unless you manually constrain the first node to follow the second node.
If you look at the deflected shape for members defined to 2 different nodes, they will deflect separately and spread apart from each other, because nothing is forcing them to deflect together. In general, the deflected shape is a great way to visually see if your model is all connected as you thought it should be.
As jayrod points out, the Full Model Merge command fixes duplicate nodes.