I've had a quick peep at that site, it's of American origin so all the info may not be relevant to Irish building practice- in particular the roof pictured looks to be shingled. Now in answer to your question - can't be certain! I assume your old fascia is timber and you are replacing with PVC or aluminium? In this case there may be a double batten behind the ex. fascia to form a tilting fillet which locks the tiles in place, in which case you're in luck. This is certainly the norm and good practice and if this is the case you're free to remove all the fascia. If not (and the fascia is holding up the first course of tiles) this is a little more difficult. However removing the fascia shouldn't cause any damage- afterall the tiles should be nailed (first row must be). However all this is subject to opening up, you won't really know til you start.