I have two separate flat objects (as the Unwrap and Flatten tool could not handle 7 faces at once in my particular shape, so had to split them) and am trying to align them with a view to merging.
I can sometimes even align with the outer edge (below), but never with the one I actually want to align to - the centre one.
Another way is to align both edges with the green axis. And the move tool can be used to seamlessly join the objects by connecting both vertexes, as Box noted well.
You can also use inferencing.
Or you could temporarily group one of the collections of edges and faces to prevent them from merging before you are ready. Lots of different options.