Added meshes will not be aligned with the current transform orientation I have put an object in its own layer to edit it separately.
Changing the transform orientation to local shows the axes of the object itself instead of the global ones.

However, if I add a new mesh, it will get a rotation of that mesh (a plane in this example) that is aligned with the global axes.
Why?

edit
Here is how I expected the plane to be aligned: to the local axes.
After selecting your 'local coordinate' object, go to Edit Mode and select a face the represents your 'floor' rotation. Shift Numpad 7 will let you align your view to the Top view of this face, and in Object mode add your new object - and in the F6 panel/ tool bar operator panel, check 'align to view' and the new object should be aligned to your 'local coordinate' object.