Yes. Build your solid model in Alibre and import it. Do a "Box Select: Surfaces" and select the entire model. Right click in the modeling screen and there is an option for "mesh parameters" or something like that. You can uncheck "Select Surface for Mesh". If you try to mesh at this point, nothing should mesh.
Then, "Point Select" the surfaces that make up the elliptical head. Right click again and re-select the "Select Surface for Meshing". Clearly, when you box select everything, you could hold the control key down, switch to a point select and deselect these so that they are not impacted by the original operation, but in the end, you just want the outer surfaces that make up the elliptical head to mesh.
Now you can mesh just the surfaces that are expected to do so. When you expand the surfaces in the tree, there is an indication as to which ones are selected for meshing, and I believe you can select and deselect them from the tree as well.
An alteranative is to build the elliptical head, but don't "hollow it out". This will give you probably 3 surfaces: the head in two surfaces and the interior face as one...the interior face my be two. Go ahead and mesh. Then, select the surface representing the interior face, right click and go to the bottom for "select subentities", choose lines and then hit delete. You may have to check to make sure that the remaining surfaces are complete and you may have to add some lines along the edge to close out the elements, but this way may be a little faster.