Add headers to each grouped section in a view
You certainly can, if you use a Views relationship to load in those other Department nodes, add a field using that relationship showing the Department node body, set it to "exclude from display" (so it doesn't appear twice) and in Format: Settings set Grouping to use that specific field. 

The key question then is - how does each Employee node know which is the Department node that corresponds to it? I'd suggest you use one of the node relationship/reference modules to link them together - I can vouch for relation which is good, powerful and (since a few months ago) works well with views. It isn't so easy to use and doesn't have a great interface yet, but learning to use it is time well spent, especially for the sort of site you seem to describe. If you think Relation is overkill (it is for many very simple sites), here's a guide which covers the many simpler alternatives.

With Relation, a step-by-step could be:


Create the relation type (say, "is in department" source>target, "has employee" target>source, valid source: employee, valid target: department)
Create a relation for each employee, linking it to its department
In the view, create a node-node Relation relationship using "is in department" from the 'source' endpoint
Add a content:body field, using this relationship. Set it to exclude from view
In View Format: Settings, choose this body field  to group the view