Airflow is a problem with fibre cement types of roofing material as you rightly say, however, they are not completely air tight.
A certain amount of airflow does pass through the surface area into the batten cavity and this is enhanced if the roof is counter-battened.
A good way of testing the permeability is to do a trial cut through the underfelt in an easy to get at central spot, a cut as depicted within this website under 'Fitting Instructions'. Physically judge the airflow and make an estimation of the passage or lack of streaming fresh air.
To do this you will need a back up repair kit of a suitable width of underfelt and fixing battons in order to restore the roof back to a sound, weatherproof state, again repair as in the fixing instructions less the vent.
Then make a decision as to your next move. You could possibly need more lapVents than would normally be used on a roof with more conventional tiles/slates if you are satisfied that there is some airflow.