You can certainly try to implements your own "org.quartz.spi.JobStore" interface using Hibernate.
Think about what you are trying to achive first though. You are attempting to write your own store layer that's already provided by working Quartz. Sure quartz is not using Hibernate, but it does what it ultimately what is asked to do: persist data into database. Quartz simply use JDBC layer without the fancy ORM layer. I suppose some advantage of using Hibernate is that you will have much more flexibility in defininig your schema and what to store in DB as objects/mapping as well.
Good luck and come back to share how your effort will go! :)