I'm trying to make TeamSpec requirements document where I have hundreds of requirements formatted in tables. So far I've been unable to make a table and use the Associate feature to Lock and Apply Template.

It works to make a template of a stand-alone table row, create a new stand-alone table row, and run Apply Template on that. But I would of course like to have a connected table with lots of table rows that I run Apply Template on. Ain't this possible?

Unfortunately, this is not possible today.  As I mention in http://meet.personifydesign.com/forums/thread/265.aspx, we will be able to do this in the future, but it will take some work and another release.