Yes you can leave the Philippines during the 10 day display notice. But get your gf to go around, ask the questions and tick all the boxes. 3 weeks is little time to arrange the whole lot in Philppines from a standing still start.
Yes you will need the seminar (well in the area where I got the licence you do anyway). But here is the issue and one of the things you need to find out. In Lapu Lapu Cebu the seminars are held only every Friday. It's this sort of detail your gf needs to find out locally before you arrive in the Philippines.
Good luck and best wishes.
