No. Only Core-MIDI USB devices will work with the Quartet’s MIDI port.
Most new USB music keyboards and drum pads are Core-MIDI devices, but this will vary from different manufacturers. Please refer to that device’s Owner’s Manual or specification to confirm class compliance with Core-MIDI.
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 Core-MIDI compliant.