I will be traveling from Sevilla to Granada and back by TRD train during Semana Santa. Are reservations necessary? (I have a railpass). It's expensive to make reservations in the US, but I'm afraid to wait until I'm in Spain - due to crowds during Semana Santa.

Somewhere else you posted that you will be in Madrid & Toledo Thursday and Friday of Semana Santa; so you are apparently asking about the earlier part of that week.
I would advise reservations on TRD's. They may be required - but you should be able to buy them the day of travel or the day before.