Is there any way in Plesk and Qmail to have any mail sent to a specific address be trashed automatically?

Yep.

The easiest way is to set up a single mailbox one one domain, but leave the mailbox checkbox UNchecked. You'll get a message in Plesk that no email will be delivered since there is no place to send it. I set it up on as null@maindomain.com pointing to the main domain for the server that everybody can use.

Then, any other addresses that you want to have all mail trashed, simply set up the mailname as a redirect like normal (no physical mailbox but with a redirect) and redirect it all over to your null mailbox address.

When mail comes in, if you're watching your maillog, you'll see it delivered to the original mailname, then redirected to the null address. Never to be seen again.

Works like a charm, thanks!