When creating a Morph map in MODO it is also necessary to add a Morph Influence for the Morph – after you create a Morph for the Mesh Item – for it to show in Renders. To do this Right Click on the Map under Morph Maps in the Vertex Map List and select add Influence. A Morph Influence will be added to the Item List with a small green icon. Now the morphs should show in renders as well as the Viewport.
Thanks to William Vaughan for clearing this one up.