Hidden unit can attack, move and cast spells, test this map for assurance.
Move Test
To make the unit hidden, press ESC key.
While ordering the unit to move to a point (better to be 1000 range and away), press ESC key.
You will notice that the SFX (Thunder Clap) will change its position, this means that the unit is actually moving while under the effect of Hide.
Attack Test
Order the unit to attack Footman.
After that, press ESC.
You will notice that the projectile of the Blood Mage will still appear even if the unit is hidden.
This means it can attack while hidden.
Cast Spell Test
While the Blood Mage is in hidden state, type the word -cast to order the Blood Mage to cast Flame Strike at the center of the map.
You can spam ESC key to hide/unhide unit.