Yes, one of the two programs can be recorded. Just start watching a recorded program as you normally do and then enable PIP as shown in this tutorial. The recorded program will go into the PIP window and you can watch live TV in the regular window. If you want to swap the programs, in other words make recorded TV big and live TV small, press the down arrow on the remote.
At one point several years ago, this didn’t work, but an update in the meantime must have quietly enabled it. I could see it being good for watching something recorded while waiting out a weather delay on a sporting event.