Is there any benefit to the trainer having a copy of the database prior to the training?
Yes. This way they can see how your system has been configured and can have their training database (if not using yours) configured the same way. By having the database in advance the functionality the users are trained on is the same as what they will see when they get back to their desks and start using the system on the live system. Dont skip this step. It is very important for the trainer to know your configuration. If they dont care to see it, get yourself another trainer. This means you will probably get a canned training that wont suit your needs.