See, I didn't RTFM! I did a google search, and here's my answer:

What happens if you don't explicitly disconnect? Since DBI handles are references to Perl objects, Perl's own garbage collector will move in and sweep up any object trash you leave lying around. It does that by calling the object's DESTROY method when there are no longer any references to the object held by your script, or when Perl is exiting.

The DESTROY method for a database handle will call disconnect() for you, if you've left the handle connected, in order to disconnect cleanly from the database. But it will complain about having to do so by issuing a warning:

Database handle destroyed without explicit disconnect.

A major caveat with the disconnect() method regards its behavior towards automatically committing transactions at disconnection. For example, if a program has updated data but has not called commit() or rollback() before calling disconnect(), the action taken by different database systems varies. Oracle will automatically commit the modifications, whereas Informix may not. To deal with this, the DESTROY method has to call rollback() before disconnect() if AutoCommit is not enabled. In Chapter 6, we'll discuss the effect of disconnect() and DESTROY on transactions in more detail.