Can I just leave PlayoutONE playing without making any playlists?

This post refers to PlayoutONE Standard.

Yes. Using the AutoDJ you can design templates for selecting audio and then switch it on. Audio selected obeys Title and Artist rotation values which you set for each type. So for example an item type Song could have a Title rotation of 20 minutes and an Artist rotation of 60 minutes whereas the item type Jingle could have a Title rotation of 10 minutes but an Artist rotation of 1 minute.

Switch on the AutoDJ and PlayoutONE will intelligently loop through the selected template to choose the audio to play.