If the component field is not filled in, it will not show up in XML of the component after the component is saved. To verify the same, try saving the component and view the source. If you do not add any value, the source tab will not even have the field. Only once you add a whitespace or some value, the field starts to show up in the source tab.
Since the field is not even there in the component, Solr cannot search and find the same.
If you add a space in the field and save the component and then search using advanced search options, you will be able to find the same. In advances options for search by schema select the schema and then in the schema field Name search by just hitting a space bar, it will give the component with blank field.
I tried it in Tridion 2013 SP1 and it works fine and finds components where I had given a whitespace in the field.
So, to make them searchable, add a default value to the schema, run component synchronizer so that you don't have to open each component after updating the schema and then Solr will be able to search for the same.