You do not need to have the Half Fare Card in possession to purchase tickets with half fare discount. You only need to be able to show it during a ticket control, ie, on the train itself. So buying a ticket now, with discount, and then getting the HFC later is indeed possible. You can even buy the HFC here at the station.
However I would not book the Jungfrau trip in advance. Just buy it here. The trains have enough capacity. You may, depending on your other plans, want to look in to local passes like the Jungfrau Travel Pass.