To get around this sort of issue, I have always created a specific Staff Role, which gives them specific rights in specific places, but not sure this will help you achieve exactly what you want. Individuals can be assigned Roles at the Category Level, but Cohorts are not. This is simply because if you have a large Cohort accessing editing capabilities at the Category level you have opened a rather large security hole in your Moodle, that's the logic behind the restriction, but not your intent.
You could try assigning a role at the Category level that allows Staff to look at the courses. Create a new Role, base it on the Guest Role, if you like, and allow that Role to be assigned at the Category level. All you need do then is to test it, with a dummy user and work out what permissions and capabilities you really want the Role to have. Or you could use the Non-editing Teacher Role as the template and restrict Capabilities until you are happy it can only do what you want to to do. That's the best answer I got, unless someone has a way of doing what you want.