Thanks Mika.
This is all new to me, so apologies for the questions that might seem silly to you. :)
Would that handle the multisite login situation?
And since posting this, discussions with the client have changed the parameters -- instead of a sidebar, we'll do a login link in a top navigation bar, and also have login required to comment (so it would be in the comment area on the bottom of posts, for example).
How do I integrate this logic in those locations?