Connect tool - it's a great tool, well... the idea of it anyways. I think the execution of the tool is a bit poor in comparison to Blender, which has the "Join" counterpart.
In Blender, even across edges between vertices you can use Join, it will automatically find the shortest path between the two selected vertices.
However in Maya, if there is an edge blocking the path of the two vertices, Maya will run into an error trying to complete that function. No connection will be made. Makes the tool fairly lacklustre, and not as robust as it can be. Usually, you would need to switch to Knife tool, which kind of defeats the purpose of connect tool.
If the tool could be improved; by whoever is in the modelling TD team there.... that would be dope!