Hi David,
Yes, you can take partial backups for database/tables and can restore it on MySQL 5.6 Community Server.
For that, you need to create tables manually on MySQL 5.6 first, DISCARD TABLESPACE, copy .cfg and .ibd file for table and finally IMPORT TABLESPACE on destination server. This feature is named as Transportable Tablespace. You can read further about it here [url]http://dev.mysql.com/doc/refman/5.6/en/tablespace-copying.html[/url]