I've been corresponding with a couple of Microsoft guys about this, and they are saying that it likely won't work until a full blown LINQ provider is available for SQLite, or LINQ to Entities is release.
For the moment, I don't believe this presents too much hardship, since the only thing that I've found so far that doesn't work is the automatic refresh of DB generated data, such as primary keys and timestamps, in the in-memory object that is used to do an insert or an update. The actual insert or update works fine in the DB itself, and subsequent queries of that data retrieve the new information correctly.
I believe that it will be possible to isolate this particular lack and work around it in most cases until such time as it can be made to work. If I can't do that, I'm a crappy programmer and should give it up anyway. :)