Does mongodb automatically move small non-partitoned databases to spread read load?
Left to its own devices, no, MongoDB will not move those unsharded databases to a different primary shard - the automatic balancing only applies to chunks from sharded collections.  

It will round robin through your shards as the databases are created to spread them out across all the shards from that perspective.  If you had one shard originally and expanded to many, the databases may have been concentrated on that shard - the round robin aspect only applies when you create the database, not the collections inside it.

Once the databases are created, and assuming you can predict what will be used and when, you can then move them to whatever shard you wish using the movePrimary command and distribute load accordingly:

http://www.mongodb.org/display/DOCS/movePrimary+Command

Naturally, this will be a quicker process if there is no data in the databases, but should still be possible after the fact.