Answering your questions:
1) No, NHibernate does not ship drivers. You have to look for them elsewhere. I, for example, use Npgsql with PostgreSQL.
2) It is very possible by changing your driver and your connection string to start using a different database without major problems (also by avoiding db specific mappings such as sequences or identity for id generation). I have migrated from SQL Server to PostgreSQL very recently; just so you have a notion of how well it went, the migrated product was querying over 70 tables with the HQL, Criteria and Linq APIs of NHibernate and we only had a problem with the collations being different in both databases, which does not concern NHibernate at all. In my opinion, as long as you stick to NHibernate for querying, you'll be safe.
Since you're leaving the choice of the database to your client, I would recommend you list and recommend only a few select databases. Your clients just might run across a bad driver, for example.