Yes they can, but I think you mean may they do it- is it against the law in some way.
I'm not sure but I can't see why anyone would take issue. Consider a department of 10 people . Everyone who works there is aware of when others are absent so it's not a big step to publish a daily/weekly list. However it may be better to put a positive spin on it by publishing attendance figures not absence data. Now if they published the reason for absence that would be a breach of confidence.
This is just my view - Buildersmate may have a more informed view though.