I just finished setting up a VPN connection with KDE's network manager, but I cannot find any way to make it run a script before it attempts to connect.

Is there some way to do this, or will I have to manually run my script each time?

As far as I know NetworkManager does not allow to run scripts before activating and deactivating a connection, only after. You need to put your scripts in /etc/NetworkManager/dispatcher.d/ (with root owner and execution permission). There is a bug entry about that in NetworkManager's bugzilla.

In Plasma NM you can use the notification system to run a script when the connection is activating, but I think the script will run in parallel with the connection activation, so it may not work as you want. There is also the problem that this does not work for system connections and the script is run as nornal user (your would need to use sudo to run it as root).