No, the Rear USB MIDI connector is only for connecting a single USB Core MIDI Device such as a USB Keyboard Controller, Drum Pad, or Control Surface.
Note that the device must be compatible with Apple's CoreMIDI. In general, MIDI devices that can be plugged into a Mac’s USB port and used without needing to install additional software or drivers are likely CoreMIDI compliant. If your MIDI devices requires software to be installed, it is likely not compliant and won't work through the Duet or Quartet’s MIDI port. In this case, we recommend you connect it directly to a USB port on your computer or through a USB hub instead.
This port will ONLY pass MIDI data. It cannot pass any other type of communications protocols, and therefore will not work with USB storage devices, typing keyboards or mouse, or devices that require a controller app to function.