Does anybody Know?

[Henry the Fifth]

What the Academy and Royal Academy do in the Spain or Portugal campaigns they don't appear to be associated with any particular units!

[FactionHeir]

They give you traits and ancillaries.

[HoreTore]

You get Tercio Pikemen and gendarmes from the spanish academies. You don't get anything other than a trait and some ancillaries from the portuguese one, so I wouldn't bother with it.