I have a local project with unit tests that have to be executed on the server I'm deploying too. How do I configure this within the project properties dialog?

My current procedure is to log in to that server via ssh, navigate to the proper folder and execute phpunit. Is PHPEd able to do that for me?

Yes, phped can do that. What you need is a remote project. If you prefer to develop locally then deploy to remote server, you will have two projects -- one for local files and 2nd for remote one. If you prefer to develop remotely too, remote project alone would be sufficient. As of how to setup remote projects, I'd recommend you to start Project Settings Wizard and proceed with 4th option -- which is at the bottom. You'll need 3 accounts:
remote file account, terminal account and debugger tunnel. All three are based on SSH. First will use sftp extension, 2nd will run shell session, 3rd will be using port forwarding to allow phpunit communicate with the IDE. Wizard will update project properties accordingly and check how they work.