is there a way to check whether the DST patch is installed on the Blackberry device on the BES?

ya, double click a user (or edit properties), then go to "blackberry device (read-only), then applications and its usually listed at the bottom like "net_rim_bb_timezoneotapatcher"

If you go to the BlackBerry DST Site there is a tool out there that you can use to find out which devices have the patch.

Keep in mind, too, that devices with OS 4.2.2 and higher already have the patch as part of the OS.