Is there a way to only add ports that are used? And can I schedule a search used ports that aren't currently monitored?

NPM has an option to only monitor active ports after discovering a switch's resources.

A potential drawback is choosing that option and then discovering your switch manufacturer may support some security protocols that end up looking like more active ports. 

You can see if this has happened by scrolling down the list of of resources and looking for ports labeled "Controlled" and "Uncontrolled."  If they're present, and if you don't want to waste element count monitoring them, you'll have to manually unselect them from the discovery and selected Active ports.

Does UDT have this same option--discover all options, but only select Active ports?

A drawback is your List Resources function must be done when most ports are active.  And it's not automatic.  It can't discover newly active ports by itself.

I bet a Thwack script expert knows how to make this happen!  Someone?  Anyone?

When adding new devices/ports via Network Discovery, you can select from groups of ports which are up, admin down, operationally down etc. You can go to also go to UDT settings> Port management and re-select whatever you are interested in.

*Bump* Is there a way to schedule a periodic scan for new volumes and interfaces?

If you turn on the scheduled discovery in the Settings page Orion will find all new or changed nodes and you'll see the newly added volumes and interfaces (as well as being able to automatically add switches to NCM for config collection and to UDT for port/user monitoring) . You'll get a regular update at the top of your admin screen that nodes have been discovered or changed and then you can then import them to Orion or ignore them. There's a list of the Ignored nodes and their volumes & interfaces, in case you change your mind and want to un-ignore them. It's best to run a number of small jobs and you need to specify each ones frequency & their subnets, IP ranges, credentials etc.